
Class t£C I^ F 



Book.. 



COPYRIGHT DEPOSm 



NEW REVISED EDITION 



The Laws of Thought 



OR 



FORMAL LOGIC 



A BRIEF COMPREHENSIVE TREATISE ON THE 

LAWS AND METHODS OF CORRECT 

THINKING 

BY 

WILLIAM POLAND, S.J. 
St. Louis University 




LOYOLA UNIVERSITY PRESS 
CHICAGO 






COPYRIGHT, 1921 
BY 

LOYOLA UNIVERSITY 
CHICAGO, ILL. 



c « c 
c c 
c e c 



V 



JUL -5 '21 



©CI.A617567 



Al^ \ 



PREFACE 



It may not be unwise to preface the following pages 
with a caution regarding their scope and purpose. Such 
caution may, indeed, be due not only to the writer lest 
his aim be misunderstood; but also to the reader, who 
might otherwise seek in this little book for what it does 
not contain. 

This book, then, is not a Psychology. It does not 
discuss the nature of the soul or of its faculties. It 
merely enumerates the principal acts of the intellect; 
and describes them as far as is necessary for the pur- 
pose of this book, which is to lay down briefly and 
clearly the process of right thinking. This requires no 
encroachment upon the field of psychology. 

Questions which should be discussed later on, in the 
course of philosophical studies, if introduced into an 
outline of correct thinking, only retard progress : firstly, 
because they are distracting; but especially because 
the mind is not prepared for them. Even after long 
discussions they are not understood by one who is just 
entering on the study of philosophy. 

Many things have been here omitted which would 
find a fitting place in an exhaustive treatise on Logic. 
But they are such things as are not necessary to the 
purpose of this compendious work. Just as there are 
many curious combinations of numbers which might be 

3 



4 PREFACE 

introduced, and sometimes are introduced, into an arith- 
metic, but which are of no essential service in forming 
an accurate and rapid accountant; so there are many 
things — curiosities — which may be introduced into a 
Logic, but which are in nowise necessary to prepare 
the mind for accurate and ready thought in the study 
of philosophy. 

On the other hand, this book is not intended as a 
sort of a ''Logic made easy," or ''Logic in twenty lessons 
without a master." In philosophy less than in other 
things can we profitably dispense with a master. 

Finally, attention is called to the fact that terminology 
is strictly adhered to, both for the sake of brevity, and 
for the sake of the learner's progress, that he may 
be obliged to understand each section before passing 
further. 

The chief revision in this edition affects Chapter VI, 
on Method. This Chapter has been re-arranged and 
has been entirely re-written. 



CONTENTS 



CHAPTER I. INTRODUCTORY. 

Page 
Article I. Logic. 

1. Logic. 2. Formal and Material Logic. 3. Natural 

Logic. 4. Artificial Logic. 5. Logic as a Science. 6. 

As an Art 9 

Article II. Three Acts of the Mind. 

7. Three Acts. 8. Knowledge Representative. 9. Sim- 
ple Apprehension, Idea. 10. Judgment. 11. Reasoning, 
Argument. 12. Oral Expression. 13. Term. 14. Propo- 
sition. 15. Syllogism 11 

CHAPTER II. IDEAS— TERMS. 

Article I. Ways of Classifying Our Ideas. 

17. Abstract, Concrete. 18. Clear, Distinct, Complete, 
Comprehensive. 19. Singular, Particular, Collective, 
Universal 15 

Article II. Classification of Universal Ideas. 

20. Form. 21. Reflex Universal. 22. Species. 2Z. Im- 
portant Observation. 24. Genus. 25. Dijfference. 26. 
Property. 21 , Accident. 28. Heads of Predicables . 17 

Article III. Subordination of Genera. 

29. The Same Form Generic and Specific. 30. Dia- 
gram. 31. Highest Genus, Lowest Species, Subaltern 
Genera 22 

Article IV. Classification and Use of Terms. 

32. Real and Logical Terms. ZZ. Univocal, Equivocal, 
Analogous Terms. 34. Univocal. 35. Equivocal. 36. 
Analogous. Zl . Supposition or Use; Material, Logical, 

Real 23 

5 



6 CONTENTS. 

CHAPTER III. JUDGMENTS AND PROPOSITIONS. 

Page 
Article I. Definitions. Structure of Propositions. 

38. Judgment. 39. Proposition. 40. Subject, Copula, 

Predicate. 41. Logical and Grammatical Predicate . . 27 

Article II. Simple and Compound Propositions. 

42. Simple. 43. Compound. 44. Various Constructions. 
45. Categorical. 46. Conditional. 47. Conjunctive. 48. 
Disjunctive. 49. Remark 28 

Article III. Immediate and Mediate Judgments. 

50. All Judgments. 51. Immediate. 52. Mediate. 53. 
The Process 31 

Article IV. Connection Between Subject and Predicate. 

54. All Judgments. 55. A Priori. 56. A Posteriori. 57. 
No Synthetic a Priori 32 

Article V. Extension and Comprehension. 

58. An Axiom. 59. Extension. 60. Comprehension. 61. 
Illustration 34 

Article VI. Extension of Propsitions. Quantity and 
Quality. 
62. Extension. 63. The Subject. 64. Note. 65. The 
Predicate. 66. Universal Affirmative. 67. One Excep- 
tion. 68. Universal Negative. 69. Particular Affirma- 
tive. 70. Particular Negative. 71. Two Laws. 72. Af- 
firmative and Negative. 73. Negative Particle. 74. 
Quantity and Quality 36 

Article VII. Related Propositions. 

75. Three Relationships. 76. Conversion. 77. Equiva- 
lence. 7S. Opposition. 79. Diagram 41 



CHAPTER IV. REASONING— ARGUMENT. 

Article I. The Syllogism. 

80. Reasoning and Argument. 81. Styles of Argument. 
82. The Syllogism. 83. Antecedent, Consequent, Prem- 



CONTENTS. 7 

Page 
isses. 84. Consequence. 85. Axioms. 86. Analysis o£ 
Argument. 87. Middle and Extremes 45 

Article II. Figures and Moods of the Syllogism. 

S8. Major, Minor, Middle. 89. First Figure. 90. Second 
Figure. 91. Third Figure. 92. Moods of the Syllogism 48 

Article III. Laws of the Syllogism. 

93. Scope of the Laws. 94. First Law: Three Terms. 
95. Second Law : Extension of Extremes. 96. Third 
Law: Extension of Middle Term. 97. Fourth Law: 
Place of Middle Term. 98. Fifth Law: Affirmative 
Conclusion. 99. Sixth Law: Negative Conclusion. 100. 
Seventh Law : No Conclusion. 101. Eighth Law : No 
Conclusion. 102. Ninth Law : Particular Conclusion. 

103. Caution . 54 

Article IV. Some Species of Syllogism. 

104. Simple and Compound Syllogisms. 105. Condi- 
tional Syllogisms. 106. Conjunctive Syllogisms. 107. 
Disjunctive Syllogisms 61 

Article V. Other Styles of Argument. 

108. Argument Abbreviated. 109. Enthymeme. 110. Sori- 
tes. 111. Polysyllogism. 112. Epichirem. 113. Dilemma 64 



CHAPTER V. TRUTH OF THE PREMISSES. 

Article I. Formal and Material Logic. 

114. The Form. 115. The Matter. 116. Value of the 
Conclusion 68 

Article II. The Demonstration. 

117. Two Kinds. 118. Direct. 119. Indirect. 120. Sim- 
ple, Compound. 121. A Priori. 122. A Posteriori . . 70 

Article III. Induction. 

123. Deduction and Induction. 124. Complete Induc- 
tion. 125. Incomplete Induction. 126. Example. 127. 
Analogy. 128. Caution 72 



8 CONTENTS. 

Page 
Article IV. Fallacies. 

129. Fallacy. 130. Petitio Principii. 131. Evading the 
Question. 132. Of the Accident. 133. A Dicto Simplici- 
ter. 134. Of the Consequent. 135. Of the Cause. 136. 
Of the Question. 137. Of Reference. 138. Of Ob- 
jections n 

CHAPTER VI. METHOD. 

Article I. Scientific Method. 

139. Scientific Method. 140. Analysis and Synthesis. . 82 

Article II. Parts. 

141. Parts: real and logical. 142. Real Parts: accidental, 
integral, essential. 143. Real Essential Parts: physical 
and metaphysical. 144. Physical Parts. 145. Meta- 
physical Parts. 146. Logical Parts 83 

Article III. An Illustration. 

147. Analysis. 148. Synthesis. 149. The Negative. . . 87 

Article IV. Analytic Table. 

150. Table. 151. Meaning of Table 90 

Article V. Definition. 

152. Kinds of Definition. 153. Essential Definition. 154. 
Some Rules for Definition 92 

Article VI. Division. 

155. Logical Division. 156. The Simple Rule 95 

Article VII. Science. 

157. Science. 158. Object of a Science. 159. Material 
and Formal Object. 160. Logical Character of a 
Science 97 

Outline of Sciences 102 

Explanation of Outline 103 

Points for Practice 104 

Index 107 



THE LAWS OF THOUGHT. 



CHAPTER I. INTRODUCTORY 



Article I. Logic. ^ 

Logic — Formal and Material Logic — Natural and 
Artificial Logic. 

1. The name Logic comes from the Greek, Xoyog. 
Aoyo? signifies reason, thought; also oral speech, a word. 
But the oral word, oral speech, is merely a sign of what 
is in the mind, of the mental word, mental speech, 
thought. Logic, therefore, has to do with thought. 

2. Formal Logic is so called in opposition to Material 
Logic, because it deals solely with the form or structure 
of thought, of an argument; and not with the matter 
contained in the structure. In the building of a house 
there are different persons or sets of persons concerned. 
Besides the architect there are those who supply and 
prepare the material, and there are the builders. It is 
the business of the architect to see that the material 
is supplied and properly prepared by one set and put 
together by the other. The builders have not to 
question the nature, value or strength of the material. 
They have only to see that the pieces fit. They 
are concerned only with the shape, the form of the 

9 



10 THE LAWS OF THOUGHT 

Structure and of each piece as tending thereto. Now, 
apply this to the edifice of knowledge. Formal logic 
has to do with the principles for the correct putting 
together of the material furnished. The general method 
of furnishing the material ready prepared is the sub- 
ject of material logic. Hence in formal logic we have 
to work at, to study, only the correct form of thought; 
not minding whether the examples we take to practice 
upon be true or not: just as one wishing to illustrate 
the structure of a bridge will take bits of wood, paper, 
straw, thread, wire or whatever he may find at hand, 
occupied solely, for the moment, with the form; and 
not at all concerned about the material. 

3. Natural Logic. Natural logic is the innate dispo- 
sition all men have to think correctly, to follow certain 
rules in the pursuit of knowledge, of truth. We are all, 
by nature, logicians. 

4. Artificial Logic. However, as sometimes, even 
with the best intentions, we are liable to think inaccur- 
ately by reason of complications of notions which arise 
?nd defects which are easily overlooked in the process of 
our thought, there has been invented what is called an 
artificial logic. Not that there is anything artificial about 
it in the sense that it is intended to replace real logic; 
but, in this sense, that it is made an art whose princi- 
ples we can learn and apply, to ensure correct thinking. 
The methods which we follow when we think correctly 
have been closely observed and have been put together 
as a connected system of rules. By learning to apply 
them we can acquire the art of logic. 

5. Logic as a Science. But logic is not merely an 
art. It is primarily a science. For these rules are a sys- 



INTRODUCTORY 11 

tematized body of fixed laws regarding the reason of cor- 
rectness in thought. Hence logic as a science may be 
defined: "The science of those laws which must rule 
the acts of the mind in correct thinking.'' 

6. Logic as an Art. Logic becomes an art when 
these laws are presented, or made ready instruments, for 
use, to ensure right thinking, to detect false reasoning, 
and to mend faulty argument. 



Article II. Three Acts of the Mind 

Simple Apprehension; Judgment; Reasoning — Idea; Judg- 
ment; Argument — Term; Proposition; Syllogism. 

7. Three Acts of the Mind. To find out the rules 
which we must follow in aiming at a knowledge of truth, 
we must consider three acts which the mind performs in 
obtaining knowledge. They are: i. Simple Apprehen- 
sion; 2. Judgment; 3. Reasoning. 

8. Knowledge Representative. All knowledge is 
representative of something real or possible. It is a 
mental expression of that something. Hence every act 
of the mind by which we know may be considered in 
two ways : either with reference to the degree of activity 
called forth or with reference to the degree in which it 
is representative. 

9. Simple Apprehension. Simple apprehension is an 
act by which the mind simply perceives or apprehends 
something without affirming or denying anything about 
it. If we consider this act as representative, as a mental 
expression of that something, it is called an idea (like- 



12 THE LAWS OF THOUGHT 

ness), a concept (the mind conceiving that something in 
itself, in Hkeness), a notion (the first element of knowl- 
edge). Thus by the act of simple apprehension we may 
have a notion, an idea, a concept, of rose, blue, plant, 
cloth, beauty, justice, etc. 

Remark that when we perceive or apprehend we do 
not perceive the idea, but the object which the idea 
represents. We do not advert, at least not especially, to 
the act of the mind. It is only by a second act of the 
mind, called reflection, that we perceive we are per- 
ceiving. 

10. Judgment. Judgment is that act by which the 
mind, having formed two ideas, affirms or denies identity 
between their objects. Thus: The rose is a plant. This 
cloth is not blue. Remark, as for the simple apprehen- 
sion, that what we affirm or deny is not about the ideas, 
but about the objects which the ideas represent. This 
is expressed by saying that we affirm or deny objective 
identity. The judgment, as the simple apprehension, 
may be regarded as a certain exercise of the activity of 
the mind, or as representative of the presence or absence 
of objective identity. As an act it is called judgment; 
as representative it is also called a judgment or a 
declaration. 

11. Reasoning. Reasoning is an act or a series of 
acts by which the mind compares (objectively) two 
cases pronounced upon in two judgments, and in that 
comparison perceiving implied the material for a third 
judgment, thereupon forms explicitly such third judg- 
ment affirming or denying according to what was per- 
ceived implicitly through the comparison. This defini- 
tion will be emade sufficiently clear for present purposes 
by two examples: 



INTRODUCTORY 13 

First example. The judgment makes two declarations : 

A man is a living being; 
Hannibal is a man. 

The mind compares these two cases and then declares 
explicitly what it perceives implied, namely: 

Hannibal is a living being. 

Second example. The judgment makes two declara- 
tions : 

A horse is a quadruped ; 

This feathered being is not a quadruped. 

The mind compares these two cases and then declares 
explicitly what it perceives implied, namely: 

This feathered being is not a horse. 

In the first example the mind worked upon the prin- 
ciple that, in the sense in which tv/o things {living being, 
Hannibal) are the same as a third thing {man), in the 
same sense are they the same as one another. In the 
second example the mind worked upon the principle that, 
in the sense in which two things {horse, this feathered 
being) are, the one {horse) the same as a third thing 
{quadruped) , the other {this feathered being) different 
from it, in the same sense are they different from one 
another. 

As in the simple apprehension and judgment the 
action of the mind was also regarded as representative, 
so the act of reasoning may be regarded as carrying in 
its third judgment a new representation of something 
perceived through the two prior judgments. Considered 
as an act it is called reasoning, argumentation, deduc- 
tion. In the other sense it is called argument, and also 
sometimes inference, conclusion. 



14 THE LAWS OF THOUGHT 

12. Oral Expression of Thought. Just as our 
thoughts are, as it were, mental words expressing certain 
objects, so in written and spoken words do we express 
our thoughts as well as the objects represented in our 
thought. 

13. Term. The oral {spoken) or written word ex- 
pressing an idea is called a term, as, blue, cloth, justice, 
beauty. 

14. Proposition. The terms, oral or written words, 
expressing a judgment are called a proposition, as, 
Hannibal is a man. 

15. Syllogism. The three propositions expressing 
an argument are called a syllogism, and also an argu- 
ment. 



CHAPTER II. IDEAS, TERMS. 

16. We shall now proceed, within the limits of the 
scope of Formal Logic, to make some considerations 
upon ideas, judgments, arguments; and upon their 
respective verbal expressions, terms, propositions, syllo- 
gisms. We begin with the most elementary, the idea. 



Article I. Ways of Classifying our Ideas. 

17. There are many ways of partitioning off into 
classes all the ideas we have or may have. 

1. Abstract and Concrete. An abstract idea is one 
which represents its object as independent of, taken 
asunder from {abstracted from), everything else. A con- 
Crete idea represents its object as coalescing with, in 
union with, grown together with {concreted) something 
else. Our ideas of blueness, wisdom, are abstract. Our 
ideas of blue, wise, are concrete, because blue, wise, are 
thought of as concreted in something else : blue sky, wise 
judge. 

18. 2. Clear, Distinct, Complete and Adequate or 
Comprehensive. According to the degree of perfection 
with which ideas express the characteristics (called 
notes) of their object, they are divided into clear, dis- 
tinct, complete and adequate or comprehensive. 

A clear idea expresses characteristics or notes suffi- 
cient to discern the object from others. A distinct idea 
distinguishes between these notes themselves. A com- 

15 



16 THE LAWS OF THOUGHT 

plete idea expresses all the notes that distinguish the 
object in reality from others. A comprehensive or ade- 
quate idea expresses all that can be perceived in the 
object: the human intellect has no such idea of any- 
thing. 

I see an object moving in the distance. I have an 
indefinite, obscure idea of something moving. It ap- 
proaches. I get an idea of my friend X — just enough 
to know that it is X without distinguishing any marks 
— a clear idea. X comes nearer. Yes, there is the walk 
and build and countenance of X. M,y idea is the walk 
and build and countenance of X. My idea is becoming 
distinct. X steps up and shakes hands with me. I know 
X intimately and thoroughly. I note all the points that 
distinguish him as X from aught else. My idea is 
complete. 

19. 3. Singular, Particular, Collective, Universal. 
Ideas may again be divided according to the number of 
individuals embraced in the idea and the manner of 
embracing them; that is, according to the extension of 
the idea. In this way we divide ideas into singidar, par- 
ticular, collective, universal. 

When one special individual is expressed in a deter- 
minate manner, we have a singular idea. Thus : Canada, 
''The President," to-day, this hook. 

When the idea expresses in an indeterminate way 
some one or other individual or some individuals, it is 
called particular. Thus: Some man or other, a man, a 
certain man, some men. 

When several objects are expressed under one idea 
or concept, but in such a way that the idea cannot be 
applied to them individually but only as a collection, the 



IDEAS, TERMS 17 

idea is called collective. Thus: A crowd, a fleet. No 
individual of the collection is a crowd or a fleet. 

When several objects are expressed by an idea, but in 
such a Vv'ay that the idea not only embraces them all, 
but is applied to them distributively and individually, 
we have what is called a universal idea. Thus : Man, 
horse, gold. I can say, Man is a living being, mean- 
ing that all men are living beings; meaning also that 
each individual man is a living being. When I say. The 
horse is a quadruped, I mean that all are quadrupeds, 
and this horse is a quadruped. When I say. Gold is a 
metal, I mean that all gold and that this piece of gold 
is metal. 

This partition of ideas being made, we have to deal 
now, in a special manner, with universal ideas. 



Article II. Classification of Universal Ideas. 

Species — Genus — Difference — Property — Accident. 
Heads of Predicables. 

20. Form. Universal ideas are classified according 
to the manner in which the one idea can be applied to 
many individuals; or, what comes to the same, accord- 
ing to the manner in which what the idea represents 
belongs to many individuals. This will explain itself as 
we proceed. Let us for the purpose of clearness and 
brevity introduce a new word, form or formality. We 
shall call form or formality whatever can be the object 
of an idea. The same thing may have many forms (or 
determinations) existing in it simultaneously. A ball 
may contain the forms of wood, roundness, whiteness. 



18 THE LAWS OF THOUGHT 

elasticity, etc. In man there are the forms of spirit, 
matter, organism, sensation, etc. 

21. Reflex Universal. Any form or formality may 
become the object of my idea. This idea I may reflect 
upon, and then regard as applicable not only to the 
individual form from which I first got it, but as appli- 
cable to an indefinite number of individual cases, actual 
or possible, and also as sufficiently representative of the 
same formality as it exists or may exist in each of those 
cases. I begin to regard the idea as universal, as 
applicable to many, by reflecting up it. The idea, as 
so regarded by reflection, is called a reflex universal idea. 
Even before I reflected upon it, even as I got it directly 
from the individual form, it was in itself capable of being 
applied to the indefinite number of cases. As such, 
prior to reflection, it is called a direct universal, 

22. Species. If a form constitutes, or if combined 
forms constitute, the whole essence of a class of indi- 
viduals, so that no individual of the class can be, or 
be thought, without said form or combination, then such 
form or combination is said to be specific, and the reflex 
universal idea representing it is called a specific idea. 
Thus the combination of rational and animal in man 
constitutes his essence. The complex idea rational 
animal regarded as applicable to all possible men is a 
specific idea. 

23. Important Observation. Now here we have 
something curious to note. The idea rational animal is 
one idea — complex, but one. Where, when we apply 
it to all men actual and possible, has it one object? 
When we speak of the rational animal, of rational ani- 
mals, of humanity, we find ourselves figuring to our- 



IDEAS, TERMS 19 

selves a certain something outside of us which is neither 
this man nor that man nor the great collection of all 
men. Yet is it something which we do put up before 
us as the object of our universal reflex idea, rational 
animal, humanity; and we talk of it a^ if it were some- 
thing, a man in general. We know that what we say of 
it is true of each case where there exists the rational 
animal, where there exists humanity. What is it? It is a 
convenience invented by the ingenuity of the mind for 
the needs of thought. It is consequent upon the innate 
tendency of the mind to pursue the most profitable and 
expeditious modes of thought. It is something we 
create in possessing ourselves of the reflex universal 
idea. It is a something that does service for all the 
individual cases. We call it the species. I know that 
the expression human species suggests to us the whole 
collection of men, and that naturalists do use the word 
species to express collections. But we do not reason upon 
collections. We should never get through. Neither do 
we reason, when speaking, for instance, of man, upon 
this man or that man. When we say man is mortal, we 
speak of man, in general, taken as a species, in the sense 
explained. 

24. Genus. If the form be something that is found 
in all the individuals of two or more classes so as to 
constitute part of the essence of such individuals, or 
briefly, if the form be found as part of the essence in 
two or more species, it is called generic, and the reflex 
universal idea representing it is called a generic idea. 
Thus man and brute agree in this, that they are both 
animal; the formality animal is of the essence of the 
species man and of the species brute. Animal, therefore. 



20 THE LAWS OF THOUGHT 

is generic, and applies to all the individuals of the two 
species. If now we put before us that certain something 
which will stand as one for all the individuals possessing 
animal nature, we shall have what is called a genus. 

25. Difference. Now take two species. They agree 
in something that is common to the essences of both. 
This, as we have said, is genus. But they differ also in 
other essentials. All the individuals of one species have 
a formality which is not in any of the individuals of the 
other, and which distinguishes all the individuals of one 
from all those of the other. The reflex universal idea 
of this formality is called a differential idea ; and as this 
stands out objectively in the species, it is called a differ- 
ence or specific difference. Take the genus animal. It 
embraces the two species, rational animal and irrational 
animal. Rational and irrational are specific differences. 

26. Property or Inseparable Accident. Sometimes 
there is found a form in all the individuals of a species, 
which form, though not of their essence, is still neces- 
sarily connected with the essence and flows from it. 
The reflex universal idea of a form so considered is said 
to be the idea of a property. Such form, considered in 
the species, as we have explained species, is named a 
property or an inseparable accident. Such may be con- 
sidered for instance, the powers of speech and of 
laughter in man. 

27. Accident. If, however, a certain form happen 
to be common to many individuals, but be in nowise of 
their essence nor necessarily connected therewith, and 
be such that it can be added or taken away without 
affecting the essence, such form is said to be simply 



IDEAS, TERMS 21 

accidental. The universal reflex idea representing it as 
so separable is the idea of an accident. The form itself, 
in whatever way considered, as thus separable, is called 
an accident. Thus the forms, blue, green, circular, 
square, thick, soft, etc., are separable accidents. We dis- 
tinguish the inseparable accidents by the special name of 
property, 

28. Heads of Predicables. The wide reaching na- 
ture of the classification which has just been given, will 
be seen if we consider that whatever we affirm or deny 
of anything is affirmed or denied as a genus, species, 
difference, property or accident. That is to say, what- 
ever we predicate (affirmatively or negatively) we pred- 
icate (affirmatively or negatively) as the genus, species, 
etc., of that of which we predicate it. Thus we say man 
is a rational animal. We predicate rational animal of 
man. We predicate it as the species. If we say man is 
rational, we predicate rational as the specific difference. 
If we say man is an animal, we predicate animal as the 
genus. If we say the man is white, yellow, strong, we 
predicate white, yellow, strong as accidental, as ac- 
cidents. Hence genus, species, difference, property, 
accident, are called Heads of predicables, because what- 
ever is pre die able of anything comes under one of these 
heads. There is a single exception to this general law. 
The exception is for the form being. Being applies to 
whatever can exist or be thought of. The idea of being 
is said to be transcendental. But the predication of be- 
ing (as also of one, true, good) constitutes on§ of the 
most subtle discussions of general metaphysics. We need 
not speak of it here. 



22 THE LAWS OF THOUGHT 



Article III. Subordination of Genera. 

Highest Genus — Subaltern Genera — Lowest Species — 

Individuals. 

29. The Same Form Generic and Specific. It is to 

be remarked that there are cases where the same form 
considered as a universal is capable of being regarded 
as both genus and species. Take, for instance, the form 
substance. Since the individuals to which it extends 
can be divided into two classes, corporal substance 
(body) and incorporeal substance (spirit), it is genus 
with reference to them, and they are species embraced 
by it. But the form corporeal substance (body) is again 
a genus when regarded as universal, for it extends to 
individuals that can again be divided into classes, — 
organic body and inorganic body. These become species 
under it. Organic body, next taken as a universal, be- 
comes a genus with reference to the classes sentient or- 
ganic body (animal) and non-sentient organic body 
(plant). These are species under it. But animal is also 
genus with reference to rational animal and irrational 
animal. 

30. Diagram. The following plan will exhibit this 
to the eye : 

Substance. 

I 



Corporeal Substance or Body. Incorporeal Substance. 



Organic Body. Inorganic Body. 

I 

I I . 

Sentient Organic Body or Animal. Non-sentient. 

Rational Animal or Man. Irrational. 

I 



I Charles, Frederic, Augustus, etc. 1 



IDEAS, TERMS 23 

31. Highest Genus, Lowest Species, Subaltern 
Genera. In this table it is seen that substance is used as 
genus only. Body, organic body and animal are used both 
as species and as genus. Man is used as species only. 

When a genus cannot be considered as a species under 
a higher genus, it is called highest genus. 

When a species under one genus cannot be made a 
genus with reference to individuals under it, that is, 
when the individuals cannot be classified as species, it is 
called lowest species. 

The forms that are predicable both as genus and as 
species are called subaltern genera. 

In the table, Substance (supposing it to be incapable 
of being ranged as species under a higher genus) is 
highest genus. Man is lowest species. Body, Organic 
Body, Animal, are subaltern genera. Charles, Frederic, 
Augustus, etc., are merely individuals of the species 
man. 



Article IV. Classification and Use of Terms. 

Real, Logical — Univocal, Equivocal, Analogous — 

Supposition. 

32. Real and Logical Terms. We may now say a 
word about terms. Terms are the written or spoken 
words that stand for ideas or for the objects of ideas. 
A term is called real when it expresses an object as that 
object may exist independently of the mind. Thus Lon- 
don, this man, are real terms. A term is called logical 
when it expresses an object in that kind of existence 
which depends entirely on the mind, as man, animal, 
used in the universal sense to stand for genus or species, 
v. gr., for animal and man in general. Genus and species 



24 THE LAWS OF THOUGHT 

as we have explained them are mental creations, doing 
service as representatives for a class, or what is the 
same, their existence is logical, dependent on the mind. 
Hence the terms expressing them as such are called 
logical terms. 

33. Univocal, Equivocal, Analogous Terms. Leav- 
ing the real terms and concerning ourselves solely with 
the logical, we find that, on account of the defects of 
language, some terms, doing service as universals, do 
not always represent the same idea nor apply in the 
same manner to all the individuals for which we make 
them stand. We find terms to be not only univocal but 
also equivocal and analogous. 

34. Univocal. That term is called univocal (one 
word) which is really but one term in meaning as well 
as in sound. That is to say, the univocal term is always 
applied with the same signification to each and all of 
the inferiors (i.e. species or individuals) to which it can 
be applied. Such are the terms, animal, man. 

35. Equivocal. But if the same written or spoken 
word, the same term, comes, in the complexity of 
language-growth, to stand for two or more different 
ideas and objects of ideas, it is called an equivocal term. 
Thus the term pen is equivocal. It is a word that serves 
equally to express different ideas and objects of ideas. 
It stands equally for a writing instrument and a cattle 
enclosure. The equivocation is sometimes in the sound 
only, as bow (a reverence) and bough. Sometimes :: 
is in the writing only, as bow (a reverence) and bow (in 
archery). 



IDEAS, TERMS 25 

36. Analogous, Again, there are terms that are ap- 
pHed to different things neither univocally (i.e. in quite 
the same meaning), nor equivocally (i.e. in quite different 
meanings), strictly speaking. The same term is used 
on account of some connection between the objects. 
The connection is called, in philosophy, analogy. The 
terms are called analogous terms. 

When the analogy or connection is merely a likeness 
between the objects, it is called analogy of proportion. 
We make this the ground for the use of the metaphor. 
We will call a man a lion on account of his courage. 
We merely abbreviate a comparison. 

There is another analogy where the connection is 
cl<3ser. We say a healthy man and also (however justly) 
a healthy climate, a healthy complexion. We affirm of 
the climate (which is the cause) and of the complexion 
(which is a natural sign) the attribute which, in its full, 
original and proper meaning, belongs only to the man. 
We have here again, strictly speaking, figures of speech. 
This analogy is closer than the mere similitude. It is 
called analogy of attribution. However, it is specified as 
analogy of extrinsic attribution, because the form that 
is attributed, health, is intrinsic to man only, belongs to 
man only, and is extrinsic to climate and to complexion, 
they being but the cause and the sign of man's health. 
But we have introduced this question only to come to 
what is called the analogy of intrinsic attribution. And 
we speak of the analogy of intrinsic attribution only as 
an aid to the understanding of a later question, the 
subtle question of the attribution of being, referred to 
in 28. Therefore — 

What is attributed may really exist in all the individu- 
als to which it is attributed, and still not in such a way 



26 THE LAWS OF THOUGHT 

that it can be attributed univocally, i.e. in the very same 
sense and manner. It exists in one independently of 
all the others, but in the others only dependently upon 
this one. Thus being is predicated of God and of 
created things: of God, independently; of created 
things, only with dependence upon the Creator. Being 
is not used univocally. It does not apply in the same 
sense to Creator and Creation. It cannot be called genus. 
Under genus the species are independent one of another. 
But this question will be treated in the General Meta- 
physics. 

37. Supposition. The supposition of a term is what 
is suh- posed by {put under) the term, what is implied 
by it or intended to be understood by it. This depends 
upon the wish of the one who uses the term. We might 
extend this subject and go back over all the various 
classification of ideas and their corresponding objects. 
We shall give but three wide divisions of the supposi- 
tion and thus close this chapter. 

The supposition is said to be material when we imply 
no more than is evident from the mere sound of the 
term or its appearance as written. Thus, when we say 
or write, Man is a word of one syllable, our use or sup- 
position of the term man is material. 

If we imply that the term is used in the universal 
sense to stand for genus or species, the supposition is 
called logical. In the sentence, Man is a rational animal, 
the supposition of the term man is logical. 

When we wish the term to stand for a reality, the 
supposition is called real. In the sentence. This man 
is temperate, the supposition of the term man is real. 



CHAPTER III. JUDGMENTS, PROPOSITIONS 



Article I. Definition and Structure of 
Propositions. 

38. Judgment. The judgment, as we have said, is 
that act of the mind by which we compare two objects 
of thought and pronounce upon their identity or agree- 
ment, affirming or denying. It is an affirmation or a 
denial. 

It is not always necessary that any appreciable time 
should be taken to compare the terms before passing 
sentence. There may be and there are cases where 
the verdict is evident at once upon the presentation of 
the terms. We see at once the identity or the disagree- 
ment. Our daily thoughts are full of instances in 
point. 

39. Proposition. We have already stated that the 
judgment as expressed in spoken or written w^ords is 
called a proposition. 

40. Subject, Copula, Predicate. A proposition con- 
sists of three parts, subject, copula, predicate. The sub- 
ject is that of which something is affirmed or denied. The 
predicate is that which is affirmed or denied of the sub- 
ject. The copula is a word or words expressive of the 
affirmation or denial, the words, namely, is, are, is not, 
are not, 

27 



28 THE LAWS OF THOUGHT 



SUBJECT. 


COPULA. 


PREDICATE. 


Man 


is 


rational. 


Knowledge 


is not 


virtue. 


Vices 


are 


detestable 


Sinners 


are not 


saints. 



The copula is a convenience of language. It merely 
stands for the agreement or disagreement that exists in 
the objects; this agreement or disagreement is perceived 
by the mind comparing the ideas, and is finally pro- 
nounced upon in the judgment. 

41. Logical and Grammatical Predicate. We must 
be careful to distinguish between the predicate of the 
logician and the predicate of the grammarian. In the 
sentence, Birds fly, the grammarian may tell us that 
fly is the predicate. The logician will resolve the sentence 
in such a way as to employ the copula. He will say, 
Birds are beings-that-fly; and with him the predicate is 
beings-that-fly. Thus the logician will transform any 
sentence to put it into logical shape. 



Article II. Simple and Compound Propositions. 

Simple — Compound — Copulative — Disjunctive — 
Conditional — Casual. 

42. A Simple Proposition contains but one principal 
subject and one principal predicate. The ship is sailing, 
is a simple proposition. We may add circumstances of 
time and place, adjectives, adverbial and relative clauses, 
without making it a compound proposition. It will be- 
come complex, but not compound. The ship that was 
made last year at New York is sailing amid icebergs that 



JUDGMENTS, PROPOSITIONS 29 

have floated from Greenland to the coast of Newfound- 
land, is still for the logician a simple sentence though 
complex. All that belongs to ship goes in as subject. 
All that belongs to sailing goes in as predicate. 

43. A Compound Proposition contains two or more 
principal subjects and predicates expressed or implied. 
Paris and Berlin are beautiful is a compound proposi- 
tion and stands for the two simple propositions Paris is 
beautiful, Berlin is beautiful. Add another predicate: 
Paris and Berlin are large and beautiful. Here we have 
four simple propositions in the compound. 

44. Various Constructions. There are various kinds 
of simple and compound propositions — various as the 
grammatical constructions invented to secure brevity in 
language, the sometimes cumbersome vehicle of thought. 
The propositions receive their names from the construc- 
tions. We call attention to a few propositions. 

45. Categorical. A categorical proposition is one 
that affirms or denies absolutely and directly. It may be 
simple or compound. Thus: Man is rational, The soul 
is not material, Prudence and Justice are virtues, Camels 
and giraffes are not insects. 

46. Conditional. A conditional proposition affirms 
or denies not absolutely, but on condition. The rain is 
coming is categorical. But, // the wind is west, the rain^ 
is coming is a conditional proposition. Remark that this 
is really a simple proposition. We do not say. The wind 
is west, the rain is coming. We merely affirm condi- 
tional connection between the two. The conditional 
proposition is also called hypothetical. 



30 THE LAWS OF THOUGHT 

47. Conjunctive. A conjunctive proposition affirms 
the simultaneous incompatibility between two cases. 
No man can spend all his money on drink and still sup- 
port his family. Here we do not affirm or deny the 
categorical propositions that he spends his money on 
drink, that he supports his family. We affirm only the 
incompatibility between the two. The proposition is 
simple, however complicated in language. The conjunc- 
tive proposition is reducible to the conditional thus : // a 
man spends all his money on drink, he cannot support his 
family. The conjunctive proposition is therefore a 
species of the hypothetical. It is always negative. It 
is called conjunctive for the sake of a name, on account 
of the conjunctive particle and which connects the in- 
compatible cases. 

48. Disjunctive. A disjunctive proposition is made 
up of two or more categorical propositions connected 
in such way by a disjunctive particle that no one is 
declared absolutely, but the acceptance of one implies 
the rejection of the others. Thus, speaking of a per- 
son's age, I may say. He is either just fifty or under 
fifty or past fifty. Suppose I declare categorically that 
he is just fifty; then the two other parts become he is 
not under fifty, he is not past fifty. However, the denial 
of one case does not imply the affirmation of the Ocher 
two. If I say. He is not just fifty, I may not therefore 
affirm both that he is under fifty and that he is past 
fifty. The remaining parts are simply left in the 
diminished disjunctive proposition. He is either under 
fifty or past fifty. The disjunctive proposition is a 
species of the hypothetical, with one part positive and 
the other part negative. Thus: // he is just fifty, he is 



JUDGMENTS, PROPOSITIONS 31 

neither under fifty nor past fifty. As the example given 
implies two such conditions, we might class it with the 
compound propositions; but this matters nothing to our 
purpose. 

4^. Remark. Here we shall leave the complex and 
compound propositions. We have mentioned the con- 
ditional, conjunctive and disjunctive, because we shall 
have occasion to refer to them when treating of the 
varieties of the syllogism. 

Henceforth in the present chapter we shall confine 
our study to the elementary proposition, the simple cate- 
gorical proposition. 



Article IH. Immediate and Mediate Judgments. 

50. All Judgments. The judgments we form are 
all necessarily either immediate or mediate. 

51. Immediate. An immediate judgment is one that 
is formed without a process of reasoning. If some one 
says to me, A whole orange is greater than half an 
orange, I do not ask him to prove it. I see the truth 
immediately, and pronounce upon it without having to 
be led to see it through the medium of other truths better 
known. Again, if I take a piece of heated iron in my 
hand, I can and do know and say at once. This iron is 
hot. I do not have to go through any other judgment 
to arrive at the knowledge that this iron is hot. The 
judgment is immediate. 

52. Mediate. On the other hand, if some one tells 
me that the three angles of a triangle are equal to two 
right angles, I do not see at once that it is so ; I ask him 



32 THE LAWS OF THOUGHT 

to show me that it is so. And he proceeds to put before 
me other propositions through which I see, until it dawns 
upon me that what he said at first is true. These other 
propositions or truths are the medium through which I 
see that the three angles are equal to two right angles. 
This judgment is therefore called a mediate judgment. 
To take another example. I hand a banknote to some 
one, as payment. He tells me, This banknote is a coun- 
terfeit. I do not perceive that the note is a counterfeit. 
He imparts to me some new knowledge, and through the 
medium of that knowledge, I too can see and say, This 
note is a counterfeit. My judgment is mediate. 

53. The Process. The process by which one judg- 
ment, proposition, is made evident through the medium 
of others is called reasoning. This will form the subject 
of the next chapter. We have still to consider, in this 
chapter, two other divisions of judgments or proposi- 
tions. This we shall do in the two following articles. 



Article IV. Connection between Subject and 

Predicate. 

A Priori, A Posteriori — Necessary, Contingent — Absolute, 
Hypothetical — Metaphysical, Physical — Analytical, 
Synthetical. 

54. All Judgments. If we consider the connection 
that exists between the predicate and the subject, we 
can classify all judgments as a priori or a posteriori. 

55. A Priori. If the predicate is such that it is al- 
ways implied in the subject, and in such way that a full 
understanding of what is meant by the subject and 
predicate is sufficient, without any experiment upon a 



JUDGMENTS, PROPOSITIONS 33 

particular case, to make us see that the proposition holds 
in all cases, absolutely, necessarily and without possible 
exception, the proposition or judgment is called a priori. 
It is seen to hold prior to any application to a particular 
case. A whole is greater than any of its parts; no thing 
can simultaneously exist and not exist, — these are a 
priori propositions. 

Such propositions are also called necessary, because 
an exception is impossible. They are called absolute, 
because they hold, absolved from, free from, all condi- 
tion. They are called metaphysical, because their truth 
does not depend upon the physical, actual order of 
things existing. They are called analytical, because by 
analyzing the subject, by taking it asunder into all that 
it implies, we will finally arrive at the predicate and see 
that the predicate belongs to the subject. 

56. A Posteriori. An a posteriori proposition is one 
in which the idea of the predicate is not implied in the 
idea of the subject. Some one says to me. This iron is 
hot. I may know all that books can teach about the 
nature of iron and the nature of heat. But all of it will 
not teach me that this iron is hot. I must have experi- 
ence of this particular case of iron and heat. After the 
test, posterior to the experience, I may affirm. This iron 
is hot. Hence the name a posteriori. 

Such propositions are also called contingent, as op- 
posed to necessary, because they may happen to be true 
or not true. They are called hypothetical, as opposed to 
absolute, because their truth depends upon a supposition, 
a hypothesis, which may be wanting. They are called 
physical, because they represent facts of the actual, 
physical order. Finally, they are called synthetic, as 



34 THE LAWS OF THOUGHT 

opposed to analytic, because they are made up by the 
synthesis, the putting together, of two ideas, terms, 
neither of which is found in the analysis of the other. 

57. Synthetic a Priori. We have here to make a re- 
mark upon an assertion of Emmanuel Kant which has 
caused a great deal of confusion in philosophy. He 
asserted that there could be a proposition which would 
be at once synthetic and a priori, and he called it the 
synthetic a priori. Kant illustrates his discovery with 
examples. For instance, he draws upon arithmetical 
addition. The proposition three and two are five, 
3 -J- 2 = 5, is with him synthetic a priori : a priori, be- 
cause it is absolute ; synthetic, because, he says, the pred- 
icate five, 5, adds on a new notion over and above three 
and two, 3 + 2. Let us see if the predicate adds a new 
idea. We repeat what we said before, that we do not 
reason with the mere sound of the voice or the mere 
appearance of marks on paper. What does the subject 
mean ? 3 means 1 -|- 1 -f- 1.. 2 means 1 + 1. 3 + 2 
means 1 + 1 + 1+1+1. 5 means 1 + 1 + 1 + 1 + 1. 
Now put down the meaning of 3 + 2 =5, and you have 
1 + 1 + 1 + 1 + 1=1 + 1 + 1 + 1 + 1. What is 
there in the predicate that is not in the subject? 



Article V. Extension and Comprehension. 

58. An Axiom. We have delayed to this point a 
very important consideration on the subject of ideas and 
terms. We have delayed it on account of its immediate 
use in the next article. In fact, we do not hesitate to 
say that the thorough understanding of the subject of 



JUDGMENTS, PROPOSITIONS 35 

the present article is the key to philosophy. There is an 
old axiom in philosophy which runs thus: The greater 
the extension, the smaller the comprehension; or The 
smaller the comprehension, the greater the extension; or 
Widen the extension, and you diminish the comprehen- 
sion; or Expand the comprehension, and you narrow the 
extension. All mean the same thing. But what do they 
mean? 

59. Extension. The extension of an idea or a term 
refers to the number of individuals to which it can apply. 

60. Comprehension. The comprehension of an idea 
or of a term refers to the number of ideas or terms 
implied in said idea or term. 

61. Illustration. Take the idea, animal It can apply 
to — that is, it extends to all individuals in which 
there is animal nature. But combine it with the idea 
rational, so as to have rational animal, or man. At 
once you shut out from its application all irrational 
animals. You cut them off from its extension. You 
narrow its extension. Why? Because you have ex- 
panded the comprehension. The idea man comprehends 
not merely animal but animal -)- rational. If you expand 
the comprehension by adding the term white, so as to 
have white man, you will diminish the extension by 
cutting off all men who are not white. And so on. 
Every new idea added represents a new requisite in the 
object that is to correspond. The more you require in 
the objects, the fewer will they be found. 

Once more take the term animal. What is its com- 
prehension? What ideas does it imply? It implies 
sensitive organic material substance. Diminish the com- 
prehension. Take away the term sensitive. You have 



36 THE LAWS OF THOUGHT 

left organic material substance. At once you have 
widened the extension so as to take in the whole vege- 
table kingdom. Diminish comprehension again. Strike 
out organic. There remains material substance. The 
extension is widened so as to take in all that is matter 
whether organic or not. Diminish the comprehension 
again. Strike out material. Substance remains. The 
extension has been increased so as to reach into the 
spiritual world. 



Article VI. Extension of Propositions — 

Quality. 

Universal — Collective — Particular — Singular. 

62. Extension. We have just spoken of extension 
in the abstract as contrasted with comprehension. In No. 
19 we saw that the same idea could be used with varied 
compass within the entire range of its extension. It 
may be singular, particular, collective, universal. 

63. The Subject. The extension of a proposition 

depends upon the extension or compass of the subject 
as used in the proposition. The proposition is named 
accordingly singular, particular, collective, universal. 
The following are examples. Singular: This man is 
virtuous. Particular: Some man is virtuous. Some 
men are virtuous. Collective: The crowd is orderly. 
Universal: Angels are spirits. 

64. N. B. In speaking of terms and propositions we 
shall often not make a distinction between singular, col- 
lective and particular, but shall call them indifferently 
by the name particular as representing any term or 
proposition that is not universal. 



JUDGMENTS, PROPOSITIONS 37 

65. The Predicate. To state clearly what we wish 
to say about the predicate, let us take four propositions, 
— two universal and two particular, — and let one of each 
kind be an affirmative proposition ; the other, a negative. 
This will give us, for instance, the following: 

1. Cats are quadrupeds. (Universal Affirmative.) 

2. Birds are not quadrupeds. (Universal Negative.) 

3. This field is triangular. (Particular Affirmative.) 

4. Some roses are not red. (Particular Negative.) 

66. Universal Affirmative. The first proposition is 
universal, because its subject is universal, i.e. taken in its 
entire extension. As to the predicate, quadruped, we do 
not directly allude to its extension. We merely assert 
that the idea quadruped enters into the comprehension 
of the idea cat. And as cat here is universal, taking in 
each and every cat, we do state that quadruped is at 
least coextensive with cat. But we do for a fact know 
that quadruped has a wider extension than cat, that cat 
covers only a part of the extension of quadruped. Only 
some quadrupeds are cats. Hence, when we speak 
according to our knowledge and say that all cats are 
quadrupeds, we wish to say that some quadrupeds are 
cats or the idea, cat, extends to some individuals not to 
all individuals in the extension of quadruped. Quadruped, 
therefore, in the discussion of the proposition is to be 
regarded as a particular term. As these remarks hold 
good for all universal affirmative propositions (one class 
excepted), we formulate the law: The Predicate in a 
universal affirmative proposition is a particular term. 

67. One Exception. The one exception is, when the 
predicate is the exact essential definition of the subject. 
Thus in the proposition, Man is a rational animal, the 



38 THE LAWS OF THOUGHT 

predicate, rational animal, is the essential definition of 
the subject, man. It is synonymous with man. Hence it 
is precisely coextensive with the subject. We can say, 
Man is a rational animal, or Rational animal is man. 
But though we say, Cat is quadruped, we cannot say, 
Quadruped is cat. Quadruped may be tiger or elephant. 
Rational animal, however, cannot be anything but man. 

68. Universal Negative. In the second proposition, 
Birds are not quadrupeds, the subject is universal, and 
hence, too, the proposition. By denial we separate the 
idea quadruped from the comprehension of the idea bird. 
So that wherever the idea bird is applicable, in its entire 
extension, there the idea quadruped is excluded. Now, 
knowing that quadruped can have its own extension, the 
proposition implies that bird and quadruped extend to 
two distinct classes of individuals. To say that birds are 
not quadrupeds is the same as saying that no individual 
bird is a quadruped. Not one bird can be found in the 
class quadruped. Not one quadruped can be found in 
the class bird. If it could, some bird would be a quad- 
ruped. What is this but to exclude quadrupeds in its 
entire extension, that is, as a universal, from the entire 
extension of the subject? As the same remarks hold 
good for all universal negative propositions, we formu- 
late the law : The Predicate in a universal negative prop- 
osition is a universal term. 

69. Particular Affirmative. In the third proposi- 
tion. This field is triangular, the subject is particular. 
Hence the proposition is particular. Referring to our 
knowledge of things, we shall find that the predicate, 
triangular, is used in a particular sense. We do not 
predicate of this field all that is or may be triangular, the 



JUDGMENTS, PROPOSITIONS 39 

entire extension of triangular; but only this particular 
case of triangular. This field is one of the things em- 
braced in the extension of triangular. Triangular, hence, 
is used in the particular sense. These remarks hold good 
for every particular affirmative proposition. Hence the 
law: The Predicate in a particular affirmative proposi- 
tion is a particular term. 

70. Particular Negative. In the fourth proposition, 
Some roses are not red, the extension of the subject, only 
some roses, is particular. Hence the proposition is par- 
ticular. The predicate red, however, is used in the uni- 
versal sense. We affirm that redness is not found in 
the comprehension of some certain roses. No one of 
these some certain roses is to be found in the entire 
extension of things that are red. We separate the 
entire extension of things that are red from these some 
certain roses. Hence, in our denial of red as applicable 
to some roses, we use it in its entire extension, or as a 
universal. These remarks hold good for every particu- 
lar negative proposition. Hence the law: The Predi- 
cate in a particular negative proposition is a universal 
term. 

71. Two Laws. Now let us put the four laws to- 
gether and make two of them. The first and third will 
give us this : The predicate in an affirmative proposition 
is used as a particular term, i.e. according to part of its 
extension. 

The second and fourth law will give us this : The pred- 
icate in a negative proposition is used as a imiversal 
term, i.e. according to its entire extension. 

72. Affirmative and Negative. We have not thought 
it necessary to state explicitly heretofore that every 



40 THE LAWS OF THOUGHT 

proposition must be either affirmative or negative. For 
all needs, up to the present, this was sufficiently implied 
in the definitions of judgment and proposition. 

73. Negative Particle. We call attention now to 
the fact that, in the negative proposition, the negative 
particle need not necessarily stand between the subject 
and the predicate. To say. Birds are not quadrupeds, is 
the same as saying, No bird is a quadruped. Both are 
negative and are understood as such. We have not to 
question the arbitrary constructions of language. Still 
be it understood that, in order to have a negative proposi- 
tion, the language must be capable of such construction 
that the negative particle not may be construed with the 
copula, is, are, so as to form with it one piece that shall 
be, not as a link between subject and predicate, but as 
a wall of separation. This is the case in the example 
given above. But the following proposition is affirma- 
tive: Not to complain in adversity is a mark of a great 
soul We may indeed say. To complain in adversity is 
not a mark of a great soul; but the two propositions are 
not identical in meaning, for we turn the predicate from 
a particular into a universal. However, we may say, 
A mark of a great soul is not-to-complain-in-adversity. 
Here the negative particle, though next to the copula, is, 
does not form one piece with it : it forms a piece of the 
predicate. The proposition is affirmative. 

74. Quantity and Quality. The extension of a 
proposition, universal, particular, etc., is referred to as 
its quantity The form, affirmative or negative, is re- 
ferred to as its quality. 



JUDGMENTS, PROPOSITIONS 41 

Article VII. Related Propositions. 
Conversion — Equivalence — Opposition. 

75. Three Relationships. We now pass on to con- 
sider the relations that may exist between certain prop- 
ositions. The relation between two propositions — iwhen 
there is any relation at all — will be one of convertibility, 
of equivalence or of opposition. 

76. Conversion. A proposition is said to be con- 
vertible into another when the subject can be made 
predicate and the predicate subject without loss of truth 
in the new proposition. Thus the proposition, No man 
is an angel, is convertible into No angel is a man. There 
are three ways of converting propositions. We may keep 
the quantity and quality unchanged; or we may change 
quantity only; or we may change quality only. The 
first called simple conversion; the second, conversion 
per accidens; the third, conversion by contraposition.. 
Without minding these traditional names, we shall ex- 
emplify the three conversions. 

Quantity and quality unchanged. This conversion may 
take place in propositions where subject and predicate 
are both universal or both particular — that is, in 
universal negative and particular affirmative; as also, in 
propositions where the predicate is the essential defini- 
tion of the subject, since the two are coextensive. Thus, 
No man is an angel is convertible into No angel is a 
man. This field is square is convertible into This square 
thing is a field. Man is a rational animal is convertible 
into The rational animal is man. 

Quantity changed. This kind of conversion may be 
applied to universal affirmative and universal negative 



42 THE LAWS OF THOUGHT 

propositions. In the universal affirmative, All plants are 
substances, the predicate is particular. If we make it 
subject, we have Some substances are plants. The uni- 
versal negative, No man is an angel, we saw above may 
be converted into No angel is a man. This being uni- 
versal, applies to each individual in the extension of the 
subject; hence we have, This angel is not a man. 

Quality changed. This kind of conversion may be 
used upon the universal affirmative and the particular 
negative. The universal affirmative. Cats are quadrupeds, 
tells us that cats are altogether within the extension of 
quadruped. Outside of the extension of quadruped, cats 
are not to be looked for. Hence the proposition is 
convertible into What is not quadruped is not a cat. In 
the particular negative, Some roses are not red, red is 
universal in its extension. Hence outside of the exten- 
sion of red there are some roses; or, Some things not 
red are roses. 

77. Equivalence or EquipoUence. A proposition is 
said to be equivalent to (equal in value) or equipollent 
with (equal in weight) another when it means the same 
thing as the other, there being no conversion of subject 
and predicate. A proposition is turned into its equipollent 
in various ways by the use of the negative particle. 
Thus, Every man is mortal is equivalent to No man is 
not mortal, etc. 

78. Opposition. To explain what is meant by oppo- 
sition, let us take the universal affirmative proposition, 
Every man is just. In order merely to contradict this 
it would be sufficient to say. Some man is not just. 
Now take the universal negative proposition. No man 
is just. To contradict this it is enough to say, Some 



JUDGMENTS, PROPOSITIONS 43 

man is just. We have in both cases an opposition be- 
tween a universal and a particular, an affirmative and 
a negative. There is opposition in both quantity and 
quality. The opposition is one of contradiction. Propo- 
sitions so related are called contradictories. Eoth cannot 
be true, simultaneously; nor can both be false, simulta- 
neously. If it be true that all men are just, then it is 
false that some man is not just. 

Opposition in quality only. When two universal prop- 
ositions are opposed in quality, i. e., one being affirm- 
ative, the other negative, as, All men are just and No 
man is just, there is not merely a contradiction of a 
sweeping statement. There is a sweeping statement to 
the contrary. The contradiction covers each individual 
in the extension of the opposite proposition. The oppo- 
sition is one of contrariety. The propositions are called 
contraries. Both cannot be true at the same time, be- 
cause each one contradicts every individual case of the 
other. However, both may be false. They may both 
claim too much in opposite directions. 

The particular propositions implied in these two uni- 
versal, that is, the particulars. Some man is just and 
Some man is not just, as opposed to one another in 
quality, are called sub contraries. Both may be true, 
since their contradictories, the universals, may both be 
false, may both assert too much. Both particulars, how- 
ever cannot be false; for if both were false, then their 
contradictories, the universals, would both be true. 

Opposition in quantity only. This is the opposition 
between a universal and particular affirmative or a 
universal and particular negative, as. All men are just 
and Some man is just; or No man is just and Some 
man is not just. There is in reality no opposition here. 



44 THE LAWS OF THOUGHT 

The particular is implied in the universal. It is a 
subaltern of the universal. Hence, for the sake of a 
name, propositions so related, the universal and its 
implied particular, are called subalterns. If the uni- 
versal is true, the particular is true. If the universal 
is false, the particular may still be true. So, the truth 
of the particular does not imply either the truth or 
falsity of its universal. But if the particular is false 
its universal is false. 

79. Diagram. Now look at the following diagram: 

Contrary. 

1. All men are just {Univ. Aff.). 2. No man is just {TJniv. Neg.) . 

C ^' 

^ X ^ 

3. Some man is jnst {Part. Aff.). 4. Some man is not just {Part. Neg.). 

SUBCONTRARY. 



1 and 2 are contraries; 3 and 4 are subcontraries ; 

1 and 4, also 2 and 3, are contradictories ; 1 and 3, also 

2 and 4, are subalterns ( 1 and 2 being called subalternant, 

3 and 4 subalternate). 

It is clear that if 1 is true, 3 is true; and that if 2 is 
true, 4 is true. But we cannot conclude from 3 to 1 nor 
from 4 to 2. 

1 and 4 cannot be both false. One must be true, and 
the other false. The same is to be said of 2 and 3. 

3 and 4 may be both true, or one true and the other 
false. Both cannot be false. 



CHAPTER IV. REASONING, ARGUMENT. 



Article I. The Syllogism. 

Argument — The Syllogism — Analysis of Argument — 
Middle and Extremes. 

80. Reasoning and Argument. We have seen how 
the idea is the element of the judgment, and thus the 
term, the element of the proposition. We have now to 
see how an argument is constructed out of propositions. 
We defined Reasoning (11) to be an act, or a series of 
acts, by which the mind compares the truths expressed 
by two judgments, and in that comparison perceives 
implied a third truth, which it accordingly expresses 
mentally in a third judgment. This process, we s-iid, 
regarded as mere mental working, is called reasoning. 
Regarded as knowledge contained in the third judgment, 
pronounced as having been implied in the two others, 
we called it inference or argumeni The propjsiiions 
which, taken together, represent in Ir^nguage the knowl- 
edge and its process, we also called argument. We shall 
use the word argument in this latter sense. 

18. Styles of Argument. There are indeed many 
combinations of propositions which are used as language- 
representations of the process of reasoning, many styles 
of argument. Different names are given to them, accord- 
in to the variety of structure. We have the Syllogism, 
the Enthymeme, the Sorites, the Poly syllogism, the Epi- 
chirem, the Dilemma. All, however, are reducible to the 

45 



46 THE LAWS OF THOUGHT 

syllogism, which is the nearest approach language can 
make towards exhibiting the working of the mind in 
reasoning. Not that we always, or usually, argue, in 
speaking or writing, with completed syllogisms. We 
abbreviate. However, we must study the syllogism in 
its completeness. We begin with it. A few words at 
the end of this chapter will then suffice to explain the 
other styles of argument. 

82. The Syllogism. The syllogism is an argimient 
made up of three propositions so connected that if the 
first two be admitted, the third must, likewise, be ad- 
mitted. Thus, 

Every plant is a substance ; 
But the verbena is a plant. 
Therefore, The verbena is a substance. 

83. Antecedent; Consequent; Premisses. The first 
two propositions taken together are called the ante- 
cedent. The third proposition is called the consequent. 
In the antecedent the evidence is stated. In the conse- 
quent the verdict is given. The two propositions of the 
antecedent are commonly called premisses (put before). 
The first is called the major premiss; the second, the 
minor premiss. For brevity's sake they are styled the 
major and the minor. The original meaning of major 
and minor, and the reason for the use of the terms, will 
be explained in the next article. 

84. Consequence. If the consequent does really fol- 
low from the premisses, we have what is called a conse- 
quence, by which we mean that the assertion contained 
in the consequent is a consequence of what was laid 
down in the premisses. If an argument is proposed to 



REASONING, ARGUMENT 47 

US in which the consequent does not follow as a conse- 
quence, the argument must be regarded as faulty. 
Hence, 

(a) If both the premisses be true, and the argument 
be rightly constructed, the consequent, called also the 
conclusion, must be true: the consequent must be ad- 
mitted. 

(b) The conclusion, or consequent, may indeed be a 
true proposition, as stated, and taken by itself ; and still, 
on account of a flaw in the structure of the argument, it 
may not really follow from the premisses. In this case 
we may admit it as an independent proposition. We 
admit the consequent, but we deny the consequen.ce. 

85. Axioms. We repeat here two axioms stated in 
No. 11. They are the bases upon which every argu- 
ment must rest. If the conclusion is an affirmative 
proposition the argument rests upon this axiom: In the 
sense in which two things are the same as a third thing, 
in the same sense are they the same as one another. If 
the conclusion is a negative proposition, the argument 
rests upon this axiom : In the sense in which two things 
are, the one the same as a third thing, the other differ- 
ent from it, in the same sense are they different from one 
another. 

' 86. Analysis of Argument. Now look at the argu- 
ment given above, namely : 

A ^ ^^^ fEvery plant is a substance (Major Premiss). 

Antecedent -<_■:. . . ,\^' t^ • x 
tBut the verbena is a plant {Minor Fremiss). 

Consequent or r Therefore, the verbena is a substance (Con- 
CoNCLUSiON \ sequence). 



48 THE LAWS OF THOUGHT 

You will find 

1. That it contains but three terms, — plant, substance, 
verbena. 

2. That one of the terms, plant, occurs twice in the 
premisses, — once in the major, and once in the minor. 

3. That the two other terms, substance, verbena, 
occur each once in the premisses, one in the major, and 
one in the minor ; and that they both occur in tlie con- 
clusion 

4. That the term plant is not found in the conclusion. 

5. That thus each term occurs twice in the argument. 

6. That the term plant, which occurs twice in the 
premises, is there compared with the two others; with 
one in the major, with the second in the minor. 

7. That a certain relationship having been discovered, 
in the premisses, between verbena and substance, by 
means of the aforesaid comparison, this relationship is 
declared in the conclusion. 

87. Middle and Extremes. The term that is used as 
a standard of comparison between the two others is 
called the middle term; or for brevity, the middle: the 
two others are called the extreme terms or the extremes, 
one the major and the other the minor extreme. We shall 
have to speak of this subject presently. 



Article II. Figures and Moods of the 
Syllogism. 

Major and Minor Premiss — Major and Minor Extreme — 

Middle Term. 

88. Major; Minor; Middle. We spoke, in the last 
article, of major and minor premiss, major and minor 
extreme, and of the middle. We called the first premiss 



REASONING, ARGUMENT 49 

the major, and the second premiss the minor, and we 
shall continue to call them so. But the first premiss is 
not always really the major, in the original meaning at- 
tached to the word; nor in the same original meaning, 
is the second always the minor. According to the orig- 
inal use of the words, the major premiss is the premiss in 
which the middle is compared with the major extreme; 
and the minor premiss is the one in which the middle 
is compared with the minor extreme. The major ex- 
treme is the one whose extension is greater than that of 
the middle. The minor extreme is the one whose exten- 
sion is less than that of the middle. This is how the 
middle came to be called middle; because, its extension 
is between the extensions of the two other terms. 

There is only one style of syllogism in which the mid- 
dle is a real middle, as just explained. This is in the 
most obvious style of construction of the syllogism (No. 
89) ; and it is from this that the names have grown into 
common use, and are applied to all syllogisms, in the 
same way, regardless of construction. We call the 
premises put first, the major; that put second, the minor: 
and we never speak of the extremes as major and minor. 
This leads to the question of figures of the syllogism. 

By Figures are meant merely the various combina- 
tions of the extremes with the middle, in the premisses. 

89. First Figure. The First Figure is the one that 
we have just spoken of. In this, the middle is made the 
subject of the premiss containing the major extreme, and 
this premiss is placed first: it (the middle) is made the 
predicate of the premiss containing the minor extreme, 
and this premiss is placed second. Thus : 



50 



THE LAWS OF THOUGHT 



Animals are living beings; (Major Premiss.) 
But lions are animals. (Minor Premiss.) 
Therefore, Lions are living beings. 

Here the middle, animals, has less extension than 
living beings (major extreme), and greater extension 
than lions (minor extreme). The following squares will 
show how one is included in the extension of the other, 
and how easily the argument proceeds on that account. 





LIVING BEINGS 








ANIMALS 








LIONS 

Minor 

Extreme 






Middle 






Major Extreme 





As our argument was stated, we proceeded within the 
extension of living beings to find animals, and then 
within the extension of animals to find lions; thence to 
conclude that lions were within the extension of living 
beings, and that living being could be predicated of lion. 
The minor premiss might be placed first, and the major 
premiss second. Thus : 

Lions are animals; 
But animals are living beings. 
Therefore, Lions are living beings. 

In this, we proceed from the minor extreme up through 
the middle to the major extreme. 



REASONING, ARGUMENT 



51 



90. Second Figure. We remark, again, that out- 
side of the First Figure, what we call middle is really 
not a middle, in the true sense, but only in the sense 
that it is taken as a term of comparison between two 
other terms. Still we keep the name, middle; and the 
other terms are called simply the extremes. 

In what we call the Second Figure, the middle term 
is used as predicate in both premisses. Thus: 



Therefore, 



Every man is mortal; 
No angel is mortal. 
No angel is a man. 



Here mortal is the middle. Man is truly minor with 
reference to mortal. But we cannot say that Angel is 
major with reference to mortal. Angel is simply ex- 
cluded by, and excludes, mortal, and hence, excludes 
the minor contained in mortal. 





MORTAL 








MAN 











ANGEL 



91. Third Figure. In what we call the Third Fig- 
ure the term of comparison is the subject of both the 
first and second premiss. Thus: 



Therefore, 



Every plant is substance; 
Every plant is material. 
Some substance is material. 



52 



THE LAWS OF THOUGHT 



Here the term plant has less extension than either of 
the other two. The meaning of middle is lost. The 
extremes are both major. 



i5\ 








PLANT 




- 




\ 



Both substance and material cover the extension of 
plant, and hence partly coincide, i.e. at least to the 
extent of plant. This will suffice on the subject of 
Figures. 

What we have to remember is' this, that in practice 
the premiss which stands first we shall call major ; the 
premiss that stands second, minor; the term that is 
used as the standard of comparison, middle; the two 
other terms, extremes. 

92. Moods of the Syllogism. By moods of the Syl- 
logism are meant the various combinations that may be 
made in the premisses, of universal, particular, affirma- 
tive and negative propositions. We should derive no 
practical utility from a discussion of the sixty-four 
possible combinations, few of which give a correct 



REASONING, ARGUMENT 53 

argument. For the sake of a completeness, which is 
not necessary, we subjoin the following remarks on 
figures and moods. 

1. There is a Fourth Figure, which is little used, and 
which it is well to avoid in argumentation. In it the 
middle is made predicate of the major proposition and 
subject of the minor. 

Every tree is organic ; 
Everything organic is substance. 
Therefore, Some substance is a tree. 

This, it will be noticed, is the same as the First Fgure 
with the position of subject and predicate inverted in 
the conclusion, and the proposition accordingly changed 
from the universal. Every tree is a substance, to the 
implied particular. 

2. If now we take the four kinds of propositions, 
Universal Affirmative, Universal Negative, Particular 
Affirmative and Particular Negative, and make all the 
possible combinations of them that can be made in each 
of the Four Figures, we shall find that there are sixteen 
possible combinations in each figure, or sixty four in 
all, — simply regarding the position of the middle and 
taking no account of the validity of the conclusion. 
These sixty-four combinations are called the Moods of 
the Syllogism. If we take into account the validity of 
the conclusion as proceeding from the premisses, we 
shall find that only nineteen of the sixty- four combina- 
tions make correct arguments. These nineteen Moods 
are thus distributed: 4 in the First Figure; 4 in the 
Second; 6 in the Third; and 5 in the Fourth. 

We shall be able to decide upon the correctness of any 
combination from the laws of the syllogism which follow. 



54 THE LAWS OF THOUGHT 



Article III. Laws of the Syllogism. 

93. Scope of the Laws. We are now prepared to 
formulate the laws which must govern the construction 
of the correct syllogism. These laws have reference to 
the number of terms, the extension of terms, the place 
of the middle term, the quantity and quality of premisses 
and conclusion. 

94. First Law. Three Terms. There must he three, 
and only three, terms, and they must be only three in 
meaning. This is evident from what has been said : that 
the conclusion of a syllogism is simply a declaration 
of identity or difference between two terms (objectively), 
which identity or difference was implied by the compari- 
son of these terms (objectively) w4th a third term in the 
premisses. It is not enough, therefore, to have the 
terms three in mere sound or written appearance. They 
must be three in meaning (objectively). Our reasoning 
is not upon sounds of the voice or upon printed letters ; 
it is upon that which is represented both by the idea and 
by the spoken and written word. If we say : 

Stores are warehouses, 
Stores can be eaten, 
Therefore, Warehouses can be eaten, 

we have three terms in sound and writing; but we have 
four in meaning; and thus there is no syllogism. If 
we say : 

Eye is the organ of sight, 
I is a personal prounoun, 
Therefore, The organ of sight is a personal pronoun, 



REASONING, ARGUMENT 55 

the terms are three in sound, but four in meaning, as in 
writing. There is no syllogism. If we say: 

Andrew Jackson is one of the Presidents, 
Franklin Pierce is one of the Presidents, 
Therefore, Andrew Jackson is Franklin Pierce, 

we have four terms, in meaning; because, One-of-the- 
Presidents is taken in two different particular senses. 

95. Second Law. Extension of Extremes. Neither 
extreme may have a greater extension in the conclusion 
than it had in the premisses. This is a consequence, or an 
application, of the first law. For if a term in the conclu- 
sion embraces more individuals than it did in the prem- 
isses, it is really a fourth term, because it stands for 
something not meant in its first use. In the following. 

Tobacco is a plant. 
Tobacco is narcotic. 
Therefore, Plants are narcotic, 

the term plant, as predicate of an affirmative proposi- 
tion in the major, is a particular term; whilst, in the 
conclusion, as subject of the universal proposition, it is 
taken according to its entire extension. There are four- 
terms: hence no syllogism. 

96. Third Law. Extension of the Middle Term. 

The middle term must be used once, at least, according 
to its entire extension, i.e. as universal. The reason : for 
if it be twice a particular, each use may embrace totally 
different sets of individuals, totally distinct sections of 
the entire extension. This would give two different 
meanings for the middle, and hence, four terms. If 
we say: 



56 THE LAWS OF THOUGHT 

Tigers are animals, 
Lions are animals, 

we may not conclude 
Therefore, Lions are tigers. 

The middle term, animals, is twice particular, covering 
distinct sections of the entire extension, animals. It is 
really two terms. 

An objection. How, then, can the middle term be 
used once universally, and once particularly? Will not 
this give us four terms? No; because what is said of 
the term taken universally, i.e. standing for all individ- 
uals, and for each and every individual in the extension, 
can also be said of this or that individual taken sepa- 
rately. An example: 

Spirit is indivisible; 
The soul is spirit. 
Therefore, The soul is indivisible. 

In the major, spirit is universal. We say that all 
spirits are indivisible; hence, that each particular spirit 
is indivisible. In the minor, we simply call one particu- 
lar spirit by its name. In the major we said any spirit. 
In the minor we make the choice that has been offered 
us directly in the major. There are only three terms. 

Of course the middle may be used twice universally 
with both premisses affirmative or with one affirmative. 
Thus: 

All fishes are sensitive; 
All fishes are shy. 
Therefore, Some things sensitive are shy. 



REASONING, ARGUMENT 57 

or, 

All fishes are sensitive; 

No fishes are men. 
Therefore, Some things sensitive are not men. 
In each case the conclusion is particular. 

97. Fourth Law. Place of the Middle Term. The 

middle term mvist not he found in the conclusion. This 
is evident from the nature of the syllogism. Two terms 
are compared, separately in the premisses, with a third 
term, in order that their identity, or disparity, may be 
expressed in the conclusion; the middle term being 
rejected, after its use as a standard of comparison. 

98. Fifth Law. Affirmative Conclusion. Two affir- 
mative premisses demand an affirmative conclusion. For 
if, in the premisses, we implicitly affirm the identity of 
the extremes, we cannot deny that identity, explicitly, 
in the conclusion. 

99. Sixth Law. Negative Conclusion. One premiss 
affirmative and one premiss negative demand a negative 
conclusion. For, in the premisses, we implicitly deny 
identity between the extremes, by declaring that one is 
identical with the middle, and that the other is not. 
Hence we have but to deny their identity, explicitly, in 
the conclusion. 

100. Seventh Law. No Conclusion. From two 
negative premisses we can draw no conclusion. If we 
say, 

Scipio is not a carpenter, 
Scipio is not a Russian, 

there is no conclusion to be drawn. We have done 
nothing but to place Scipio outside the extension of the 



58 



THE LAWS OF THOUGHT 



two extremes; but there is nothing from which to infer 
whether there be, or be not, Russians among the car- 
penters, or carpenters among the Russians. All we can 




Carpenters 



Russians 



say is what has been affirmed explicitly, that Scipio is 
neither a Russian nor a carpenter. 

The same holds if the premisses are two negative uni- 
versal propositions. All the terms will be universal. The 
middle term, in its entire extension, will be outside the 
entire extension of each extreme. 

No star is a elephant ; 

No elephant is a wheelbarrow. 

No Conclusion. 

101. Eighth Law. No Conclusion. From two par- 
ticular premisses we can draw no conclusion. For they 
will be either, 1, both negative; or 2, both affirmative; 
or 3, one affirmative and one negative. 

First case: both negative. This is settled by the 
seventh law. 

Second case: both affirmative. In this case the sub- 
jects are particular, as we have particular propositions ; 
and the predicates are particular because the proposi- 
tions are affirmative (No. 71). Hence the middle term 
is not taken once universally, and the third law is 
broken. 

Third case: one affirmative and one negative. Then, 
according to the sixth law, the conclusion will have to 



REASONING, ARGUMENT 59 

be negative. The predicate of the conclusion will thus 
be universal (No. 71). As this predicate is one-of the 
extremes, it must, by the second law, be universal in the 
premisses. But in the. premisses there is only one place 
for a universal term ; that is, as predicate of the negative 
premiss. The particular affirmative premiss cannot have 
a universal term, and the subject of the particular nega- 
tive premiss must be particular. Now if this one place 
in the premisses where a universal term can be, be taken 
by one of the extremes, the middle term will not be, 
cannot be, used universally at all. Hence this third 
case is an impossibility, and the eighth law holds. 

We must here make an exception for the case where 
both premisses are singular. In this case there may be 
a conclusion. Thus: 

Mars is a planet; 
Mars is uninhabited. 
Therefore, One planet is uninhabited. 

The reason is that the term. Mars, being applicable 
to one individual only must be used in its entire exten- 
sion, and hence, as subject in both premisses, has the 
value of a universal: so that the two premisses may be 
treated as universals. 

102. Ninth Law. Particular Conclusion. // one 

premiss be particular, the conclusion must be particular. 
Of course, by the eighth law, one premiss must be uni- 
versal. The possible cases with one premiss universal, 
and one particular, are: 

1. With both premisses affirmative; 

2. With one premiss affirmative, the other negative; 
and in the second case we have an alternative. We 
may take a universal affirmative and a particular nega- 



60 THE LAWS OF THOUGHT 

live; or we may take a universal negative and a par- 
ticular affirmative. 

1. Making both premisses affirmative, we shall have, 

Universal Affirmative )with subject universal and predicate 

particular) ; 
Particular Affirmative (with subject particular and predicate 

particular). 

There is but one place for a universal term. This 
must be for the middle {Third Law), The extremes 
are both particulars in the premisses. Hence the subject 
of the conclusion must be particular {Second Law) ; and 
the conclusion, a particular proposition. 

2. Making one premiss negative and one affirmative, 
we shall have either 

Universal Affirmative (with subject universal and predicate 

particular) ; 
Particular Negative (with subject particular and predicate 

universal). 

Or, 

Universal Negative (with subject universal and predicate 

universal) ; 
Particular Affirmative (with subject particular and predicate 

particular). 

In either case there are two places for a universal. 
One place must be for the middle {Third Law). The 
other place will be for the extreme which is predicate of 
the conclusion; the conclusion being negative, since 
one premiss is negative. The subject of the conclusion 
must therefore be an extreme, used particularly in the 
premisses. It must be particular in the conclusion 
{Second Law), and will make the conclusion a particular 
proposition. 



REASONING, ARGUMENT 61 

103. Caution. Here we leave the laws of the syllo- 
gism Certain correct syllogisms may be adduced which 
may seem to contravene the laws. But if the propo- 
sitions of the syllogisms thus presented be examined, 
it will be seen that certain propositions, apparently 
particular, are really universal ; and certain propositions, 
apparently negative, are really affirmative, or vice versa. 
But let it be kept in mind that we reason not with mere 
words as they sound or appear on paper, but with what 
they stand for; and words, by tricks of grammar, may 
be made to obscure a thought in the presentation. In 
the same way, syllogisms with ill-drawn conclusions may 
be made to appear in keeping with the laws. But study 
the sense of the propositions. 



Article IV. Some Species of the Syllogism. 
Conditional — Conjunctive — Disjunctive. 

104. Simple and Compound Syllogisms. We have 
hitherto, for the sake of clearness, given examples of 
syllogisms composed of simple categorical propositions 
only. Such syllogisms are, as their component proposi- 
tions, called simple. One compound premiss is sufficient 
to make the syllogism compound and equal to as many 
simple syllogisms as there are simple categorical propo- 
sitions compounded into that premiss. We do not pro- 
pose to treat of compound syllogisms. We should never 
end. Attention is called here to three complexities in 
the syllogism, to which we alluded in No. 49. 

105. Conditional Syllogisms. In these the major is 
a conditional proposition (46) ; for instance, this, // they 



62 THE LAWS OF THOUGHT 

are studying logic, they are training their minds. The 
first member of the conditional proposition is called the 
condition; the second, the consequent. The minor may 
affirm the condition categorically: 

They are studying logic. 

Then the conclusion must affirm the consequent cate- 
gorically : 

They are training their minds. 

Or the minor may deny the consequent: 

They are not training their minds. 

Then the conclusion denies the condition: 
They are not studying logic. 

Note. 1. The denial of the condition will not necessitate the 
denial of the consequent. This (the consequent) may be true for 
other reasons. In the present instance they might be studying 
grammar or geometry without logic; and they would still be 
training their minds. 

2. Hence affirmation of the consequent does not always neces- 
sitate affirmation of the condition. There may, as we said, be 
other conditions from which it (the consequent) would follow. 
They may in the present instance be training their minds by 
studying other matters than logic. 

106. Conjunctive Syllogisms. In these, two incom- 
patible propositions are proposed in the major by means 
of a conjunctive proposition (47). The minor denies 
one, and the conclusion affirms the other. Example: 

No man can spend all his money on drink and still 
support his family; 

But he spends all his money on drink. 

Therefore, 

He does not support his family. 



REASONING, ARGUMENT 63 

What we said about looking into the meaning of the 
proposition and not being deceived by tricks of construc- 
tion is of service here. The conjunctive proposition is 
really equivalent to a conditional, thus, // a man spends 
all his money on drink, he is unable to support his family; 
and with regard to affirmation and denial of condition 
and consequent must be treated as such. 

107. Disjunctive Syllogisms. In these the major 
puts all the alternatives of a case in the disjunctive prop- 
osition (48). If the minor makes choice of one, the 
conclusion will be the denial of all the others. If the 
minor denies all but one, that one will be affirmed in the 
conclusion, etc. 

Example : He is either just fifty or under fifty or past 
fifty; 
But he is just fifty; 
Therefore, He is neither under fifty nor past fifty : 
Or But he is neither under fifty nor past fifty ; 

Therefore, He is just fifty : 
Or But he is not just fifty ; 

Therefore, He is either under fifty or past fifty. 

In the last casfe, as we have three possibilities, and the 
minor denies one only, the two others remain as a dis- 
junctive proposition in the conclusion. This form of 
syllogism may also be reduced to the conditional with 
one member positive and the other negative. // he is 
under fifty, he is neither just fifty nor past fifty. 

The disjunctive syllogism is useful in controversy and 
investigation. But it is, at the same time, capable of 
treacherous application for the spread of error in history 
and physical science, by the use of disjunctive majors 
which are not complete. The disjunction should state 



64 THE LAWS OF THOUGHT 

all the possibilities of the case. The members should 
have marked lines of division, and not run into one 
another. All the members may not be true; neither 
may all be false. 



Article V. Other Styles of Argument. 

Enthymeme — Sorites — Polsyllogism — Epichirem 
— Dilemma. 

108. Argument Abbreviated. We said (No. 81) 
that when we write and speak we do not always, nor 
even usually, carry on an argumentation with completed 
syllogisms. We abbreviate. The various methods of 
abbreviation give us various styles of argument, which 
have, respectively, their proper names. 

109. Enthymeme. If we drop one premiss in the syl- 
logism, the argument is called an ethymeme. Example: 

All liquids flow; 
Therefore, This tar will flow. 

We have dropped one evident premiss, this tar is liquid, 
to avoid being tiresome. 

Enthymeme originally meant a probable argument; 
but, by a mistake as to its derivation, it came to be 
applied to the argument where one premiss is kept in 
the mind. In this sense alone is the word now used. 

110. Sorites. (Piled-tip argument.) When we put 
down three or more premisses and, then, one conclusion 
following from them, the argument is called a Sorites, 
It abbreviates by dropping intermediate conclusions. It 
presumes the evidence of the conclusion after the first 
two premisses, and adds a third premiss as a minor to 



REASONING, ARGUMENT 65 

the second premiss considered as a major; then a fourth 
premiss as a minor to the third premiss considered as a 
major, etc. Thus: 

He who desponds ceases to labor; 

He who ceases to labor makes no progress; 

He who makes no progress does not reach the end. 

Therefore, 

He who desponds does not reach the end. 

It is easy to see that this is an abbreviation of two 
syllogisms. Thus : 

He who desponds ceases to labor; 

He who ceases to labor makes no progress. 

Therefore, 

He who desponds makes no progress. 

The next syllogism begins with this conclusion as a 
major : 

He who desponds makes no progress; 

He who makes no progress does not reach the end. 

Therefore, 

He who desponds does not reach the end. 

As the Sorites involves so much argument, and pro- 
ceeds so rapidly, we must be cautious with an adversary 
who uses it. The sorites may be drawn out to any 
length. Each implied syllogism must observe the laws 
of the syllogism. 

111. Polsyllogism. If we argue with a chain argu- 
ment, as in the Sorites, but in such a way that we bring 
out the intermediate conclusions, not explicitly twice as 
above, but once, to be used, simultaneously, as conclusion 



66 THE LAWS OF THOUGHT 

to the two preceding premises, and as major to a fol- 
lowing minor, our argument is called a Poly syllogism. 
The preceding example, as a polysyllogism, will be: 

He who desponds ceases to labor; 

He who ceases to labor makes no progress. 

Therefore, 

He who desponds makes no progress; 
He who makes no progress does not reach the end. 
Therefore, 

He who desponds does not reach the end. 

112. Epichirem. If a premiss, or even each premiss, 
requires proof, and the proof is attached to it immedi- 
ately, whether in substance or in full, the argument is 
called an Epichirem {taking in hand the doubted premiss 
at once). Example: 

One who denies the existence of God and a future 
life cannot be trusted in society; because he ad- 
mits no motive to restrain him from evil when 
he can do the evil without temporal inconven- 
ience. 

But the atheist denies the existence of God and a 
future life. 

Therefore, 

He cannot be trusted in society. 

113. Dilemma. The Dilemma is a double argument 
in the compass of a single syllogism. It may be even 
triple, quadruple, etc. The major is a disjunctive prop- 
osition. The minor takes up each member of the dis- 
junction, separately, and an equally satisfactory conclu- 



REASONING, ARGUMENT 67 

sion is drawn from whichever member is chosen. Thus 
a schoolboy might argue, to escape his evening study: 

To-morrow morning it will be either raining or not 
raining. 

If it be raining, I will have an excuse to stay at 
home. If it be not raining, I can use my per- 
mission to take a day at the fair. 

Therefore, 

Whatever the weather may be, I shall not have to 
go to school; and hence I need not study my 
lessons to-night. ^ 

The Dilemma is sometimes a very useful form of 
argument for a summary refutation of false theories. 



CHAPTER V. TRUTH OF THE PREMISSES. 



Article I. Formal and Material Logic. 

114. The Form. We have seen what is required in 
the quaUty and quantity of the premisses, and in the 
extension of middle and extremes, in order that a given 
conclusion may be taken as lawfully drawn from given 
premises. If I say. 

Every steamboat is a sunflower, 
Every sunflower is a violin, 
Therefore, Every steamboat is a violin, 

and suppose the premisses to be true, I have to accept 
the conclusion, inevitably, from the premisses. The 
conclusion is in perfect accord with all the laws of the 
syllogism. All that formal logic has shown us to be 
necessary in quality, quantity and extension has been 
. — supposing the premisses true — strictly attended to. 
Yet every proposition in the strange argument is false. 
This leads us to speak of the matter of the premisses, 
as affecting the acceptance of the conclusion. We shall 
say something, therefore, on the truth of the premisses. 
It may be urged that the subject does not belong strictly 
to the formal logic. The formal logic has to deal, strictly 
speaking, only with the form, or structure, of argument 
necessary to have a conclusion rightly drawn from pre- 
misses; — the matter, or truth, of the premisses being 
left out of consideration. And for this reason is it called 

68 



TRUTH OF THE PREMISSES 69 

formal logic. By this is it distinguished from material 
logic. 

115. The Matter. Material logic will teach us what 
care must be taken in the use of the various means we 
have of arriving at the truth, that is in the use of our 
various faculties; and when we may cease examining, 
and rest reasonably secure in mind as to the truth or 
falsity of what is expressed in a proposition. So that, if 
we should meet w4th a syllogism such as the following, 

Every timepiece is made of brass, 
All brass is organic matter, 
Therefore, Every timepiece is made of organic matter, 

material logic would have to tell us how to use our 
faculties, — that is, how far to trust the various faculties 
— in our search for truth in the propositions. It is only 
when we have decided as to how far we are to admit 
the propositions that the work of formal logic begins. 
Nevertheless, we begin the study of philosophy with 
formal logic, because we have had so much practical 
experience in the use of our faculties, that we already 
hold securely that many propositions are true, many 
others false, and many, again, doubtful; and we want, 
at once, a safe and systematic rule for arguing from the 
known to the unknown. Therefore we study formal 
logic first. 

However, we shall here make a short consideration 
upon the truth and falsity of the premisses, and upon 
the corresponding adhesion of mind which we can give 
to the conclusion. Yet we shall do this in such a way 
as not to touch the question of the means we have for 
arriving at the truth. 



70 THE LAWS OF THOUGHT 

116. Value of the Conclusion. We cannot hold to 
the conclusion any more firmly than we hold to the prem- 
isses. Supposing the form of the syllogism to be correct, 
if we are certain of the truth of the major and minor, 
we may be certain of the conclusion. If we have a 
lingering doubt as to the truth of either major or minor, 
that doubt will cling to the conclusion. If either major or 
minor be false, the conclusion is false ; and the argument 
is called a sophism or a fallacy. Sophism or fallacy is 
in the matter, not in the form. A defect in the form is 
called a paralogism. This has been abundantly treated 
in the preceding chapter (Nos. 80-102). 

When the major and minor are both truths of which 
we are certain, the argument is called a demonstration. 

Leaving aside the probable argument, we shall treat 
of the demonstration and of fallacies. 



Article II. The Demonstration. 

Direct — Indirect — Simple — Compound — A Priori 
— A Posteriori. 

117. Two Kinds. A demonstration is an argument 
in which the conclusion is drawn from premisses of 
whose truth we are certain. It may be direct or indirect; 
and either kind may be a priori or a posteriori. 

118. Direct. In the direct demonstration we draw 
the conclusion we desire, directly from the premisses 
where we have compared its subject and its predicate 
with a middle term. Thus: 

The soul can think; 
Matter cannot think. 
Therefore, The soul is not matter. 



TRUTH OF THE PREMISSES 71 

119. Indirect. In the indirect demonstration, in- 
stead of drawing our conclusion as coming dirctly from 
premisses in a syllogism, we show that the contradictory 
cannot be true, by exhibiting the absurd consequences 
that would follow from such contradictory. The indi- 
rect demonstration is of frequent use in geometry, 
where we show absurd consequences that would follow 
from not admitting the theorem laid down. 

120. Simple; Compound. A demonstration is called 
simple when the whole argumentation is finished clearly 
and satisfactorily with a single syllogism. If, however, 
it be necessary to bring forward new syllogisms to prove 
the major or minor or both — which may not be clear, 
or may be called in question — and, perhaps, again, new 
syllogisms to prove the new majors or minors, the 
demonstration is called compound. All the longer theo- 
rems in geometry are illustrations in point. 

121. A Priori. An argument is called a priori when 
it advances from premisses which state truths that are 
prior in the nature of things to the truth stated in the 
conclusion. Thus we may advance from what we know 
about the nature of a cause or agent, to establish some 
conclusion regarding the nature of the effect it may 
produce. The name a priori is used, also, for an argu- 
ment where we advance from principles in their wider 
extension to an application of the same principles in a 
less wide extension; as, for instance, from principles 
regarding the whole animal kingdom to conclusions 
respecting elephants and kangaroos. Likewise, when- 
ever we advance from principles to facts, as from the 
general truths about triangles to the exhibition of the 
truths applied in a particular given triangle. 



72 THE LAWS OF THOUGHT 

122. A Posteriori. The a posteriori demonstration 
proceeds in the opposite direction. It advances from 
what is posterior in the nature of things to what is prior 
in the nature of things. From the existence of an effect 
it concludes to the existence of a cause ; from the nature 
of an effect to the nature of the cause. It rises from a 
given fact to the principle that must explain the fact. 
We have an illustrious example of the a posteriori argu- 
ment in the discovery of the planet Neptune. After a 
quarter of a century of observations made upon the 
planet Uranus, discovered by Sir W. Herschel, it was 
found that its movement did not correspond with the 
known forces of gravity acting upon it, especially from 
Jupiter and Saturn. There was a fact: movement. 
The movement must have a cause. The cause must 
be a heavenly body. The movement was of such a 
character, said Leverrier, that if it came from a single 
heavenly body, that body, at a given time would be 
found in a given point of the heavens. The telescope 
is directed, at the given time, to the given point; and 
there is found the planet Neptune ! 



Article III. Induction. 
Complete and Incomplete Induction — Example — Analogy. 

123. Deduction and Induction. We add here a spe- 
cial article about a peculiar kind of a posteriori argu- 
ment, which, by custom, has been allowed to appropriate, 
as it were, the name Induction. Every a posteriori argu- 
ment is, indeed, an induction, as opposed to the a priori 
argument, which is a deduction. Deduction means the 



TRUTH OF THE PREMISSES 73 

drawing out of a particular proposition or conclusion 
from the universal premiss. Induction, on the contrary, 
is a leading back to the universal from the particular. 
Every process of thought from the particular to the 
universal is inductive. We wish to speak of induction, 
in the usual and limited acceptation of the word, as 
signifying an argument which passes from a uniform 
experience of several individual cases to a universal 
conclusion covering them all. The induction may be, 
as it is termed, complete or incomplete. 

124. Complete Induction. The induction is called 
complete when after having really made an examination 
of all the cases of which there is question, and having 
found that the same proposition, varying only the sub- 
ject, is applicable to each case individually, we draw a 
conclusion in which we include them all in a single 
universal proposition. If, for instance, I, an American, 
step into a railway car and finding there five men. A, 
B. C, D, E, I discover gradually that A is an Ameri- 
can, that B is an American, that each of the five is 
an American, and conclude that all the men in the 
car are Americans, I go through the process of a 
complete induction. The complete induction is the 
exact reverse of a detailed deduction, in which, from the 
universal, that all the men in the car are Americans, I 
would conclude: A is an American, B is, G is, D is, E 
is, I am an American. 

We may sometimes think we have a complete induc- 
tion when, in reality, we have not. We are liable to 
overlook particular cases. Moreover, sometimes even 
when the greatest care is taken in the observation of 
facts in certain branches of the natural sciences, when 



74 THE LAWS OF THOUGHT 

all the known facts have been classified under a general 
proposition, some new discovery will show that the 
general proposition is untrue, and that the induction was 
not as complete as it was believed to be. 

125. Incomplete Induction. It is to the incomplete 
induction, which bears the name in the strictest sense, 
that we wish to call particular attention. It is a process 
by which, from experience of a limited number of cases, 
we pass on to formulate a universal law. Thus we 
formulate the laws of gravitation, of equilibrium, of re- 
flection, of refraction, from a very limited number of 
cases; and we hold these laws to be applicable, as 
universal propositions, to cases tried and untried. Is the 
process lawful? 

We inquire more particularly into the matter because 
some modern logicians, of the school of experimentalists, 
make the study of induction the chief business of logic. 
The process ef thought may be accepted as lawful, — the 
experiments having been rightly conducted, — but, upon 
one condition. The condition is, that we admit the 
reality of such a thing as cause. This very condition, 
which is absolutely necessary to the valility of the process 
of induction, is not accepted by the great champion of 
induction among the experimentalists, Mr. J. Stuart Mill. 
The process, then, is lawful if we admit true causality; 
namely, that whatever begins to be, depends for its exist- 
ence upon some real influence exercised by something 
else in bringing it about. In other words. Every effect 
demands a cause. 

Recognizing this, we may set to work with experiment 
and observation at the process of induction. If we find, 
by repeated test, that the same consequent follows the 



TRUTH OF THE PREMISSES 75 

same antecedent constantly and uniformly in whatsoever 
circumstances or adjuncts of time, place, quality or rela- 
tion the antecedent may be tried, and in all the variations 
of circumstances by composition, opposition, etc. ; if we 
find, on the other hand, that, suppressing the one ante- 
cedent in question, whilst leaving all the circumstances 
and adjuncts the same, the said consequent does not 
make its appearance in any of the cases when the ante- 
cedent is so suppressed; if, again, varying the antece- 
dent, in the various cases, in quantity, intensity, direction, 
etc., we find that the consequent varies proportionally in 
quantity, intensity, direction, etc. ; in other words, if we 
find that said consequent follows said antecedent only, 
but always, and in regular proportion, — we are bound to 
recognize as really existing in said antecedent a certain 
power whereby it brings into existence the said conse- 
quent; and, also, in said consequent, a certain real 
dependence for its existence upon the antecedent. We 
perceive the two to be related as cause and effect. But 
yet more. We perceive that the antecedent is cause by 
reason of something inherent to its very nature ; for we 
have made our observations, tests, experiments, abstract- 
ing from it everything but its essential, inherent nature. 
But the essential, inherent nature of that thing must be 
present always where that thing is; the same yesterday, 
to-day, to-morrow. Hence we conclude that the same 
thing will produce the same effect to-morrow as to-day. 
We formulate a universal law which reaches to the 
future. Mr. J. Stuart Mill has, of all writers, written 
best upon the manner of making the tests for an induc- 
tion. But as he does not recognize the reality of cause, 
as he puts no real connection between foregoing and fol- 
lowing, his conclusion is universal only to the extent of 



76 THE LAWS OF THOUGHT 

the tests actually made. What he builds up with one 
hand he tears down with the other. 

126. Example. Allied to induction is what is some- 
times called the argument from example. It concludes 
to the universal from a few cases ; and, even, it may be, 
from a single case, without the tests and observations 
prescribed for induction. Its value is rather in discovery 
than in proof. A superior, well trained and vigilant 
mind will often suspect, and even detect, the universal 
law in a single case; but it will be necessary to go 
through the various tests, to make the law acceptable to 
the ordinary intelligence. In general use it is an argu- 
ment weak in point of logic. Logically, it suggests at 
most the possibility of a case. Jt is resorted to in ora- 
torical discussion. The orator has the advantage of 
forcing his listeners on without giving them time to 
examine, and urges them to act under the impression of 
a possibility. 

127. Analogy. The argument from analogy is still 
less reliable, logically, than the argument from example. 
It is a pure figure of rhetoric, a parallel between two 
cases of quite different orders. It is useful to persuade 
an audience that cannot listen to dry argument, but can 
listen very well to a story, and then follow out the appli- 
cation of the story, in all its details, to the question 
under treatment. 

128. Caution. In philosophical argument be wary in 
the use of example and analogy. It is so easy to give 
illustrations and to make comparisons. Therefore have 
we so many self-styled ''scientists," to-day, setting them- 
selves up as professional discoverers, and flying to con- 
clusions which the slow, careful processes of induction 
do not warrant. 



TRUTH OF THE PREMISSES 77 



Article IV. Fallacies. 

Begging the Question — Evading the Question — Accident 
— A Dicto Simpliciter, etc., — Consequence — Cause — 
Question — Reference — Objections. 

129. Fallacy. We have distinguished the Fallacy or 
Sophism from the Paralogism. The paralogism is an 
argument with a flaw in the form. A conclusion, true 
in itself, may be found in a syllogism which is faulty in 
the form. The conclusion may be true, indeed, but it 
has not been proved. We have previously considered 
arguments, with regard to the correctness of the form 
(Laws of the Syllogism). This article has reference to 
the matter of the conclusion. Any argument with a 
false conclusion is a fallacy. The word, however, is 
applied, in its special sense, to falsely concluding argu- 
ments which have so much the appearance of correct- 
ness as easily to deceive the unwary or to silence those 
whose limited knowledge or intelligence does not enable 
them to detect the deceit. We shall not consider any 
fallacy which is an evident violation of the laws of the 
syllogism. Every equivocation is such, since it uses a 
word in two senses, and thus gives us four terms in the 
syllogism. We subjoin some fallacies arising from the 
matter. 

130. Petitio Principii or Begging the Question. 

This is to insert cleverly and covertly into the premisses 
the very thing that has to be proved. This is a favorite 
fallacy of demagogues haranguing listeners whose hearts 
are already in the conclusion. Communistic gatherings 
echo with arguments like this: 



78 THE LAWS OF THOUGHT 

"All men are born into the world, equal, with equal 
rights to live, equally, upon the earth and to enjoy an 
equal share of the spontaneous productions of the earth. 
So that by Nature herself are they justified in asserting 
their equality against all comers. 

''But all the existing laws of society are in open con- 
flict with the equal rights of men and are framed only 
to increase the inequality. 

''Therefore, as we cannot get the rights of our equal- 
ity from society, we are by Nature herself justified in 
overturning governments and helping ourselves.'' 

Here, you see, the right to plunder is assumed covertly 
in order to justify plunder. 

The circulus vitiosus (vicious circle) is of the same 
order as the petitio principii. We prove, for instance, the 
fall of the apple from the tree by gravitation; and, later 
on, we establish gravitation by the fall of the apple. 

131. Evading the Question (ignorantia elenchi). 
Under this head may be ranged all those tricks of argu- 
ment by which one tries to make the best of his case 
without offering proof; or to shirk an objection without 
showing it to be invalid. This may be done by assuming 
for proof or disproof something similar or analogous to 
the point in question; or by attacking an opponent on 
the ground that he is not to be regarded as an authority 
on the subject (argumentum ad hominem), thus arous- 
ing prejudice against his argument; or by appealing to 
the passions of the reader or listener; or by trying to 
shame an opponent out of the debate by citing against 
him authorities that have the respect of the listeners. 

This is an utterly illogical way of proceeding, but it 
may be followed with great effect. 



TRUTH OF THE PREMISSES 79 

132. Fallacy of the Accident. This consists in as- 
suming as essential what is purely accidental. Thus a 
man might argue against Christianity because some who 
profess it are not exemplary in their conduct. However, 
evil-doers are never such by reason of Christianity ; they 
may be, in spite of it. 

133. A Dicto Simpliciter ad Dictum Secundum 
Quid, and vice versa. This is the fallacy of arguing 
from an unqualified statement to the same statement 
qualified, or vice versa. This fallacy pervades daily con- 
versation. From the unqualified statement that a man is 
learned the popular mind jumps to the conclusion that 
he is learned in particular matters to which, perhaps, he 
has never given any attention. How many a man truly 
''learned" has had to pay for his name as ''learned'' by 
being consulted as though he were an encyclopaedia? 
This fallacy works with equal success in the opposite 
direction. An exhibition of some knowledge in a few 
particular matters is soon .made the basis for the con- 
clusion that the exhibitor is "learned." 

134. Fallacy of the Consequent. This consists in a 
misuse of the conditional syllogism. Thus some one says : 
// the gale is strong to-night, the tower will fall. In 
the morning the tower is found to have fallen. The 
fallacy infers that the gale was strong. The truth is 
that the tower may have fallen under other agencies. 

135. Fallacy of the Cause. This lies in assuming as 
the cause of something that which is merely an accom- 
panying or preceding circumstance, or at most an occa- 
sion. Thus we sometimes read in the newspapers that 
the political principles of a party in power are the cause 
of all the fluctuations in trade. Therefore, to secure 



80 THE LAWS OF THOUGHT 

Steady business, the administration must be changed. 
And when the administration is changed, and the same 
difficulties occur, the responsibiUty is shifted to the op- 
posite principles of the new party in power. Or we read 
that the cause of a bank robbery was the insecure system 
of bolts put on by a certain safe company, thus shifting 
the responsibility from the want of vigilance on the part 
of the authorities, and from that education of the head 
without the education of the heart, so prolific in evil- 
doers. 

136. Fallacy of the Question. This consists in 
asking a number of questions all of which are evidently 
to be answered in the same way, by yes or no ; and then 
very deftly inserting one question whose answer should 
be the opposite, but which is made to pass along with the 
others, as answerable in the same way. Thus the com- 
munistic orator: ''Are we poltroons Shall we reject 
the equality nature has bestowed upon us? Shall we 
see the products of the earth, which nature intended for 
all, piled up for the use of a few? Can we, as nature's 
freemen, refuse to vindicate our equality? Is there 
anything to prevent us from destroying? They refuse 
us a share in their millions. Shall we refuse them a 
share in our poverty? etc. Therefore, etc.'' 

137. Fallacy of Reference. This is untruth — the 
inventing of false references for the support of a propo- 
sition. People do not usually verify references, and 
hence may be easily deceived by a long array of author- 
ities [ ?] cited at the foot of the page. 

138. Fallacy of Objections. This consists in pour- 
ing forth a volume of objections, one immediately after 



TRUTH OF THE PREMISSES 81 

another before giving opportunity for reply. The adver- 
sary's time may be more than taken up in trying to 
answer one of them. Even then his long, careful answer 
may not be as effective with the audience (or reader) as 
the terse, captious objection; and besides, the other 
objections will be carried away unanswered. 



CHAPTER VI. METHOD. 



Article I. Scientific Method. 

139. Scientific Method. When an object of thought 
is presented to us for investigation our task will be to 
discover v^hat propositions we may formulate regarding 
it. What may we predicate of it? Of what may it be 
predicated? When a proposition is presented to us in 
study, reflection, reading, conversation, debate, we may 
be concerned to know whether it is true or false. How 
shall we find out? When we make an assertion, having 
no doubt of its truth, how shall we proceed, if called 
upon, to place it in evidence by means of a demonstra- 
tion? When we are provided with certain truths and 
we wish to see if they can be made available for research 
or for the establishment of what we have been accepting 
as true or for the rejection of what we have been pre- 
suming to be false, how shall we proceed? The answer 
to all this is to be found in the application of the laws 
of thought to the matter in hand. And this is what is 
meant by scientific method, the means of arriving at 
scientific knowledge, science. It is an inquiry into the 
connection or opposition of ideas, of terms. 

140. Analysis and Synthesis. Scientific method 
is ultimately reducible to two processes, analysis and 
synthesis. Analysis (greek, dvd^ixrtg ) means taking 
apart. Synthesis (greek, oirv&EOig ) means putting to- 

82 



METHOD 83 

gether. Hence we have the names, analytic m,ethod and 
synthetic method. The two processes are often inter- 
woven and the name will then indicate the process that 
prevails in an investigation. Analysis and synthesis have 
to do strictly with parts, being the taking asunder and 
putting together of parts to see what use may be made 
of such parts, separate or conjoined, as subjects or 
predicates in true propositions. 

We may form a general idea of the meaning of the 
words, analysis and synthesis, from the work of the 
chemist. When the lump of crude matter is brought to 
him with the request that he find out what is in it, 
he separates it into its elements. He analyzes. His 
process is analysis. On the other hand, when he puts 
together chemical elements to get a chemical combina- 
tion, he synthetizes. His process is synthesis. But, as 
we said, one main process may be supplemented by the 
other. To be sure of the character of something found 
in the analysis the chemist may test it by synthesis, that 
is, by observing whether it will combine with some 
known element to form some known compound. 



Article H. Parts. 

141. Parts: Real and Logical Parts. In general 
the word, part, is used to indicate anything that enters 
in any way into any combination real or fanciful which 
is considered as a unit. That combination, taken as a 
unit, is called a whole in reference to such parts. Parts 
are either real or logical. The whole made up respect- 
ively of such parts is called a real or logical whole. 



84 LAWS OF THOUGHT 

Real parts are those that really exist in some whole 
which may have a real existence. A house is a real 
whole and the foundation and roof are real parts. Log- 
ical parts do not exist really inside the logical whole. 
The logical whole is simply a general idea and the 
logical parts are all the things to which that idea applies. 
The idea, tree, is a logical whole; and everything it ap- 
plies to whether existing or not is a logical part. The 
entire construction is mental, logical. 

142. Real Parts: Accidental, Integral, Essential. 
Real parts are accidental if they can be removed, re- 
stored, modified, without interfering with what we re- 
gard as the identity of the unit as a whole. Such, for 
instance are the shape or hardness of an identical lump 
of wax. But we must remark that there may be parts 
which can, indeed, be removed without interfering with 
the identity of the unit, yet which are always under- 
stood to belong to its natural completeness, and these 
are called integral parts. Thus a man may lose a finger 
and still retain his indentity as the same man, but there 
will be something wanting to his completeness. Essen- 
tial parts are those which must all be present in order to 
have the given unit whole. There are two kinds of real 
essential parts. 

143. Real Essential Parts: Physical and Meta- 
physical. Real essential parts are those that must be 
really, actually, in the unit in order that it may exist or 
even be thought of. Now we may look at these 
essentials in two different ways, so that for the same 
unit whole we shall get two sets of essential parts, each 
set, however, by itself constituting the whole. These 
two sets are called respectively physical parts and meta- 



METHOD 85 

physical parts, and the whole as looked at in the one or 
other way is called correspondingly, a physical whole or 
a metaphysical whole. 

144. Physical Parts. Real essential physical parts 
are essential parts into which the real whole is physically 
separable. They can be actually separated and if one is 
disjoined there is an end to the unit whole. For in- 
stance if an animal be cut in two so that the brain be in 
one piece and the heart in another, there will be a sepa- 
ration of essential physical parts. The animal will cease 
to exist. 

145. Metaphysical Parts. We can consider that 
same animal as a unit whole made up of real essential 
parts which are physically inseparable from one an- 
other. Still these parts are real and actually existing in 
the whole, and as so combined they constitute the whole 
in its essential unity. We can think of them separately, 
but we cannot take them asunder physically as we would 
the brain and heart of the animal. They are named 
metaphysical parts. The prefix meta (greek, fietd ) in- 
dicates that they are aside from the physical condition 
of separability. Of all the real parts mentioned it is 
only these metaphysical parts that we take account of in 
scientific method, in analysis and synthesis. 

These metaphysical parts are simply those requisites 
which answer to the several ideas that go to make up the 
comprehension of the idea of the unit whole. Take for 
instance the object, animal. The idea of this object as 
a unit whole will be the idea, animal. What is compre- 
hended in the idea, animal? That idea implies or com- 
prehends the idea of substance, the idea of something 
material (matter), the idea of something organic (organ- 



86 LAWS OF THOUGHT 

ism), the idea of sentient power (feeling, sensation). 
These ideas make up the entire comprehension. No one 
may be omitted. Each one answers to something that is 
real in the object. xA.ll these realities in the object as 
combined constitute the essentials of the object unit 
whole. They are therefore real essential parts. But 
they cannot be taken asunder. They are beyond the 
possibility of physical separation. The power of feeling 
in the animal cannot be detached from the substance, nor 
organism from the matter. These metaphysical parts 
are the real essential parts we have to take account of in 
analysis and synthesis. 

146. Logical Parts. The other kind of parts which 
are taken account of in scientific method are the logical 
parts. Take that same idea animal as representing the 
real animal, a metaphysical whole. We may look at that 
idea as a universal idea which is applicable to many 
cases. The idea thus taken in its universal sense is 
called a logical whole and all the things to which it ap- 
plies, of which it can be predicated, are its logical parts. 
These things, these parts, may exist or they may not 
exist. The greater number will never exist. The idea 
embraces all in the universality of its application. It 
embraces all possibilities. For this reason logical parts 
are also called potential parts. Hence, these parts are 
not things that have a real existence within the logical 
whole. The logical whole is only a general idea, and the 
logical parts are the things possible or actual to which 
that idea can apply. The logical whole represents the 
entire comprehension of the idea animal, all that it im- 
plies; and the logical parts will make up the extension 
of the idea, everything to which it applies. 



METHOD 87 

The construction is altogether mental. The logical 
whole is an idea. The logical parts are the things pos- 
sible of which it may be predicated. It embraces them 
all in its meaning, in its extension. The one same idea, 
animal, representing a real metaphysical whole, is re- 
garded in its uuniversal logical sense as being applicable 
to all animals thinkable in the past, present or future. 

To conclude, therefore, the parts that must be consid- 
ered in scientific work are the metaphysical parts which 
are the parts of comprehension, and the logical parts 
which are the parts of extension. 



Article III. An Illustration. 

147. Analysis. We are not treating of any partic- 
ular science but only of method. We are, therefore, using 
the same example throughout in order to avoid confu- 
sion; and we are using only so much of the example as 
is necessary to our purpose. Analysis and synthesis have 
to do strictly with parts. The investigation of any object 
of thought must begin by analysis or synthesis; and it 
must advance either continuously by the process first 
used, or by changing from one process to the other as 
circumstances may prompt. A simple example will serve 
to illustrate the mental movement in either process. 

Let us suppose, for instance, that we wish to know 
something about animal. What is animal? This ques- 
tion is an express wish to use the term, animal, as the 
subject of a proposition. We wish to predicate some- 
thing of it. We wish to predicate of it all that must 
necessarily be predicated of it. To do this we must sep- 



88 LAWS OF THOUGHT 

arate it mentally into its real, essential, metaphysical 
parts. We shall then have everything that must neces- 
sarily be predicated of animal. This separation may be 
begun variously in as much as one mind may give first 
attention to one characteristic, and another mind to an- 
other. The actual knowledge of the investigator will be 
of service to him in helping him to pick out the char- 
acteristics in the best order. 

To begin, then, we may presume that our attention is 
first attracted by the fact that animal has the power of 
sensation. We find this everywhere in what is called 
animal, and nowhere outside of what is called animal. 
It is an essential character, an essential part. We say, 
therefore, that animal is sentient. We ask what does 
this sense power imply, what does this act of sensation 
imply? We find by investigation that amid all varia- 
tions it implies some kind of general organism of the 
being and a particular instrument or organ for each dif- 
ferent kind of sensation. We say, therefore, that organ- 
ism is an essential character in animal, a metaphysical 
part. Animal is organic. We see readily that organism 
is always matter. Hence we say that animal is material. 
We know that matter is substance, sornething underlying 
the material accidents of color, shape, etc. Hence, ani- 
mal is substantial. Do we see anything beyond? No. 
We have mentally separated the real metaphysical whole 
into its real metaphysical parts. Animal is sentient, or- 
ga7iic, material substance. The process has been analy- 
sis. The process is always analysis when we proceed 
from the subject. 

148. Synthesis. If we start from what is to be used 
as a predicate the process will always be synthesis. If 



METHOD 89 

we wish to discover, for instance, what subjects sub- 
stance may be predicated of, what things may be called 
substance, or, to keep the same example, whether sub- 
stance may be predicated of animal, our process will be 
synthesis. We take this idea, substance, as a logical 
whole and we try to find out whether in its extension it 
reaches to animal as one of its logical parts. We experi- 
ment by adding to substance other ideas that will com- 
bine with it in order to see if we can arrive at a combi- 
nation that will give us all the essential parts of animal 
so that the idea, animal, as representing the metaphysical 
whole may be considered to be a logical part in the ex- 
tension (the application, the classification) of substance. 
The process is nothing more than that of going back 
mentally through the analysis and predicating succes- 
sively of the whole the parts that belong to it and into 
which it has been separated. 

Now, of course, we all know that animal is substance. 
This knowledge belongs to our most primary perceptions. 
But if we did not know, how should we find out by 
starting from substance ? We should have to add to sub- 
stance notions compatible with it to see if we might 
reach a combination which a competent person would 
recognize as constituting animal. Beginning, then, ac- 
cording to our knowledge, we say that substance must be 
material or immaterial, one or the other. Let us go first 
in the direction of matter. We find that matter must be 
either organic or inorganic. Let us go in the direction of 
organic matter. We find that organic matter is again 
of two kinds, sentient or non-sentient. We choose to go 
by way of sentient. Here we are told to stop for we 
have reached animal. Animal is sentient, organic, mate- 
rial substance. 



90 LAWS OF THOUGHT 

149. The Negative. What we have said applies also 
to the negative proposition. We must start from the sub- 
ject by analysis and we must start from the predicate by 
synthesis. May we say, animal is mineral? In the essen- 
tial metaphysical parts of animal we do not find min- 
eral. Hence, from the analysis of the subject we must 
say, animal is not mineral. If we try the predicate for a 
synthesis we may add to mineral all that is compatible 
with it but we shall never get the combination that gives 
animal, hence, again, animal is not mineral. 

Finally, in a proposition we cannot reverse subject and 
predicate unless subject and predicate have both exactly 
the same comprehension and the same extension, that is 
to say, unless they indicate exactly the same thing, no 
more no less, in different words. 

What we have been saying will be seen plainly indi- 
cated in the following table. 



Article IV. Analytic Table. 



150. ■: 


Cable. 








Substance. 

1 




1 Material. 

1 


Immaterial. | 




1 Organic. 






Inorganic. | 




1 Acid. Salt. Base. | 


1 Sentient 


(Animal). 

1 






Non-Sentient ( Plant ).| 

1 


i Vertebrate. 


Articulate. 


Molluscan. 


Radiate. | 


1 Flowering. Flowerless. | 



I Mammal. Bird. Reptile. Amphibian. Fish. 



151. Meaning of Table. A term, written or spoken, 
stands for idea and for thing, that is, for the logical 



METHOD 91 

and the real whether whole or part. What then do the 
terms as they lie on the table indicate? They show that 
comprehension and extension are opposites. The com- 
prehension of a term takes in everything above it, — mov- 
ing upward always but never past the middle and down 
again. The extension of a term takes in everything below 
it, that is, on every side always moving downwards. 
Start at any term on the table. We may look at it as a 
metaphysical whole and as a logical whole. We get its 
metaphysical parts, its comprehension, going upwards. 
We get its logical parts, its extension, going downwards. 
Hence everything on the table if considered as a meta- 
physical whole will have substance as an essential part 
in its comprehension. At the same time substance, as a 
logical whole, will have everything on the table as a log- 
ical part in its extension. Comprehension, going up- 
ward, gives us all that enters into the essential meaning 
of the term. Extension, going downward, gives us a 
classified arrangement of all that the term can apply to. 
As we go up the table, from term to term, comprehen- 
sion diminishes because at each step a requisite is elimi- 
nated. At the same time the extension increases with 
each step upward, the field of application below becom- 
ing wider and wider. Contrariwise, as we go down the 
table the extension diminishes because we are cutting off 
from the field of application. At the same time compre- 
hension increases because at each step down we are add- 
ing a new requisite (above), a new essential part. 

We may here call attention to a statement which may 
be confusing if not rightly construed. It is said that 
analysis proceeds from the less universal to the more uni- 
versal at the same time that it proceeds from the com- 
plex to the simple. There is no contradiction. The first 



92 LAWS OF THOUGHT 

part of the statement refers to extension and the second 
part refers to comprehension. Anaylzing, for instance, 
animal, we shall find that any one of the essentials will 
have a wider extension, application, than the extension 
of all the essentials taken together. The extension of 
animal is not so wide as that of substance. On the other 
hand considering comprehension the combination of es- 
sentials in animal is something more complex than any 
one essential which is necessarily more simple in its 
make-up. 

In actual study and inquiry, then, comprehension will 
give us what the term necessarily means, no more no 
less. It will provide us with the essential definition of 
our subject. Extension will give us a classified arrange- 
ment of the field covered by the term. It will give us the 
exhaustive logical division of our subject. 



Article V. Definition. 

152. Kinds of Definition. Correct definition, exact, 
precise, definition should always be aimed at. Insistence 
on exact definition is the only way to security and clear- 
ness in argument. There are various kinds of explana- 
tions which are called definitions. There is but one kind 
with which we are here concerned. This is the real, 
essential, metaphysical definition. This table will show 
the various kinds of definition. 



Definition. 

I 



1 Nominal. Real. 
I 



Descriptive. Genetic. Essential.] 

I 



Physical. Metaphysical. 



METHOD 93 

A nominal definition is an expression in words of the 
meaning which for any reason whatsoever happens to be 
attached to a term whether arbitrarily by the speaker or 
by common though incorrect use or by the agreement of 
the best writers and lexicographers, etc. The definition 
is nominal also when the literal meaning of a word is 
given according to its derivation. Thus we say that in- 
finite, from the Latin in (a negative particle) and finis 
(a limit), means without limit. The word is looked at 
from the viewpoint of grammar, etymology, etc. 

A real definition is the expression in words of the 
nature of an object. The attention is fixed upon the 
object which is to be definitely represented in words. 
Such definition may be descriptive, genetic or essential. 
A descriptive definition is nothing more than what is 
named description in treatises on literary composition. 
It does not enter into the essence of the object. It merely 
presents, at the choice of the writer, such combination of 
salient features as may make the object recognizable, 
and fix it in the imagination. It is thus variable accord- 
ing to the mind of the writer and its purport is not 
scientific. A genetic definition (from genesis, origin) 
is the expression in words of the manner in which an 
object is produced. A genetic definition of a circle 
would be : a plane surface generated by revolving a line 
about one of its extremities. It does not enter into the 
essence. 

153. Essential Definition. An essential definition 
names in combination all the essential parts of an object. 
It has been noted (No. 143) that the same object may be 
regarded as made up of separable essential parts, called 
physical parts, or as made up of inseparable essential 
parts, called metaphysical parts. . The enumeration of 



94 LAWS OF THOUGHT 

these physical parts will give us the physical definition. 
The enumeration of these metaphysical parts will give 
us the metaphysical definition. This real essential meta- 
physical definition is the one to be aimed at in logical dis- 
course. It is the perfect scientific definition. It gives 
all that is in the comprehension of the thing; hence, a 
thoroughly comprehensive definition. 

To formulate this metaphysical definition it is not nec- 
essary to make explicit mention of each of the meta- 
physical parts. Two will be sufficient. We have seen 
(Table, No. 150) how each term implies all the terms 
above. Hence we will take one term to indicate the gen- 
eral class to which the thing to be defined immediately 
belongs and we will qualify this term, by a term in the 
row immediately below, thus excluding all the other 
terms in the row. If we take organic as a general class 
(genus) and sentient as special class (species) to exclude 
all the other species in the row, we shall have a defini- 
tion by proximate genus and ultimate difference. This 
is the metaphysical definition of animal. An animal is 
a sentient organic being. 

154. Some Rules for Definition. 1. In philo- 
sophical matters insist on the essential metaphysical defi- 
nition. It may sometimes be useful to begin with another 
kind of definition; but never lose sight of the meta- 
physical. 

2. The terms of any kind of definition should convey 
a more definite idea than the single term expressing the 
thing defined. This does not mean that every term in 
the definition should be at once better known by every- 
body than the single term. When we define a circle to 
be a plane surface with a single curved line for a boun- 



METHOD 95 

dory, every point of which is equally distant from one 
fixed point on the surface, our definition may be less 
intelligible to some persons than is the term circle. But 
one who learns the meaning of the terms in the defini- 
tion will find that his idea of circle has become more 
definite. 

3. Try to so word the definition that it may be con- 
vertible by simple conversion (No. 76) with the term ex- 
pressing the object defined. Thus: if a circle is a plane 
surface . . . etc., then a plane surface . . . etc. 
(as above) is a circle. 

4. Do not define by a negation, by saying what a 
thing is not. However, a negative term may sometimes 
call for definition as, for instance, the term injustice. It 
is made up of a negative particle, in, and a positive part 
which is excluded by the negative. We define the posi- 
tive part justice. The definition will represent the posi- 
tive part as excluded. 

5. Use words in their exact meaning; and when there 
is a choice of words use such as may be most readily 
understood by the persons immediately addressed. 



Article VI. Division. 

155. Logical Division. As the scientific definition 
of a term or subject is given by combining the meta- 
physical parts of comprehension, so the scientific division 
is made by indicating the logical parts of extension. 
When we define we look at the term as a metaphysical 
whole. When we divide we look at it as a logical whole. 
Take any term on the Table (No. 150). If we combine 



96 LAWS OF THOUGHT 

it with what is above we have the definition of some- 
thing. When we consider it as taken asunder into the 
parts below we have the logical, the scientific division of 
the same something. 

The logical division is made by first placing the term 
in question as genus, as highest genus. (See No. 29 to 
No. 31.) We may, for instance, wish to divide matter. 
As genus it will be divided into species. This is done 
by separating it into kinds according to qualifying dif- 
ferences that do not overlap. These differences are 
called specific differences and the kinds so qualified are 
called species. The differences should be chosen as 
furnishing the fewest immediate divisions of the whole 
genus. Matter is thus divided into organic matter and 
inorganic matter. After such division is made it may 
be found that each species can serve as a genus and be 
divisible into its own species. Perhaps one species will 
serve as a genus and another will not. But we go on 
dividing in the same manner in every direction until no 
new species can be made a new genus divisible into spe- 
cies or kinds. Each species will then be found to be 
divisible only into individuals all of one kind having the 
same specific difference. 

156. The Simple Rule. In every correct division 
the parts must be found to be precisely equal to the 
whole. In a logical division, therefore, the sum of the 
species must cover precisely the field that is covered by 
the genus. This implies that there must be no over- 
lapping. We may not place as species anything that 
covers the whole genus ; and each species in a division 
must be characterized by a difference which separates 
it totally as a part from each of the other species. If 



METHOD 97 

plants were to be divided into growing plants and food 
plants the first member would cover the genus since all 
plants grow. If animals were to be divided into wild, 
vertebrate, dangerous and tropical there would not be a 
complete division and there would be some overlapping. 

The advantage of correct logical division in the study 
of any matter is evident. It maps the subject in a way 
that insures both order and completeness. It can be 
applied in any study. Though other divisions may have 
to be resorted to as temporarily expedient and in lack of 
detail, the logical division should be kept in mind. 

In this chapter we have been using a single example 
as summarized in the Table (No. 150) in order to fix in 
the memory the respective distinctions between, meta- 
physical and logical whole; metaphysical and logical 
parts; comprehension and extension; analysis and syn- 
thesis; definition and division. In the readiness of our 
knowledge of these distinctions we shall find the best 
test of our knowledge of the principles that underlie the 
laws of thought. 



Article VII. Science. 

157. Science. What we have learned about the ways 
of correct thought will be valuable to us in any kind of 
study. Every perception of truth is knowledge. If this 
perception be through a demonstration it is scientific 
knowledge. A complete body of related truths regard- 
ing a given object as presented by demonstration is called 
a science. The knowledge of that body of truths as so 
related and demonstrated is the knowledge of the science. 



98 LAWS OF THOUGHT 

158. Object of a Science. By the name, object of a 
science, we mean not an end or purpose, but the thing, 
the object that is studied. And the same thing as a gen- 
eral groundwork or object of study may provide us with 
the particular object of more than one science. It may 
be considered under aspects that are quite distinct one 
from the other, and we may thus get distinct sets of con- 
nected truths — each set being in itself complete. In other 
words, we may consider separate characters which are 
found to affect the totality of the same general object. 

159. Material and Formal Object. The thing in 
general which furnishes the material for study is called 
the material object of a science. The particular char- 
acter, the formality, studied, or this formality as affect- 
ing the material object, is called the formal object of the 
science. We may say for instance that the whole cor- 
poreal universe is the material object of both astronomy 
and chemistry. But the formal object of the science of 
astronomy is the mass, magnitude, distance, co-ordinated 
motions, etc., of the various masses of matter, called 
heavenly bodies, which make up the corporeal universe; 
whilst the formal object of chemistry is the substantial 
distinction between the elements of matter and their 
respective capacities for substantial union with one 
another. 

Things even the most varied and of different orders 
miay be brought together as the material object of one 
science by reason of a same formality or characteristic 
running through them all and making the formal object 
of the science. Thus spirit, matter, substance, accident, 
and whatsoever is or can be, and whatsoever can be 
thought of as ''something," will make up the material 



METHOD 99 

object of the science of Ontology. Ontology is the 
science of being (greek, oiv, ov, ovtog ). The character, 
"being," "something," runs through not only what exists 
but also through whatever can be thought of. It is the 
formal object of the science of Ontology. 

160. Logical Character of a Science. Looked at in 
their purely logical aspect, and considered solely in re- 
gard to the kind of mental work dominating, sciences 
are distinguished as belonging to one or another of two 
classes, the analytic or the synthetic. Again, in the log- 
ical aspect, they are distinguished as being either in- 
ductive or deductive. Moreover the analytic are spoken 
of as inductive, and the synthetic as deductive. This 
does not mean that induction is the same as analysis, nor 
that deduction is the same as synthesis. Analysis and 
synthesis refer strictly to the mental work on terms with 
the view of getting propositions. Induction and deduc- 
tion refer strictly to the mental work on propositions 
with the view of getting conclusions. The explanation 
of analysis and synthesis has been given in this chapter. 
The explanation of induction and deduction is given in 
Chapter V. A science is logically characterized by the 
kind of mental work with which it begins and which pre- 
vails in the building up of the body of related truths 
(No, 157). 

Some sciences grow by analysis and induction: first 
by analysis of terms to get particular propositions, then 
by induction to gather (induct) concordant propositions 
into a general law. All purely experimental sciences are 
established in this way. Thus beginning with particular 
objects, we observe, analyze, note agreements, and finally 
formulate general propositions which represent what we 



100 LAWS OF THOUGHT 

call laws, for instance, of motion, light, heat, equilib- 
rium, etc. 

Other sciences grow by synthesis and deduction. In 
these we begin with known general laws from which we 
draw (deduce) consequences. Using each new evidence 
gained we go on to draw more remote consequences. In 
this way, for instance, starting from a few recognized 
general truths regarding lines and angles we go on by 
the search for relations and combinations to build up the 
science of geometry. The synthesis consists in the put- 
ting together of ideas, terms, until there is found a valid 
combination in a logical conclusion. 

Analysis is the way of discovery. It reveals, lays open, 
discovers the invariability of a given truth in ever vary- 
ing circumstances. This truth is then certified to as a 
general truth, as a law, by the argument of induction. 
Synthesis is the way of invention. Starting with the 
general truth, the general proposition, it joins one of the 
terms to a new term to get a minor which will serve with 
the first proposition used as a major. It then joins the 
extremes for a consequence. It thus finds an applica- 
tion of the general law. The application is also certified 
to by the argument of deduction. 

Further discussion of this matter would be confusing. 
In an analytic science it may frequently be of service to 
have recourse to synthesis; and in the synthetic science, 
to analysis. The student will find an aid to methodical 
thought in looking over the tables of contents in standard 
text-books of various sciences. It must be noted, how- 
ever, that in the teaching of the purely experimental 
(analytic, inductive) sciences the tedious process of 
growth from which they take their name is not strictly 
followed. It would be an interminable work for the stu- 



METHOD 101 

dent were he obliged to hear the story of the experi- 
mentation that was needed to discover each general law. 
When the general law has been fully established it is 
much simpler in teaching to present the law first and then 
to show its generality by chosen illustrations which will 
suffice to indicate the ground for a valid induction. 



102 



CO 

o 
u 

CO 

O 
2 

H 
D 
O 



vo 



o 
I— I 

O 



w 






H 






.M 






52; 






1— 1 


►:? 




fe 


<1C 




iz; 


H ?s 




1— 1 








IDE 
acci 






O"" 


P 




Q 


P-H 


H 


< 




H 




s 1 


"izi 


, ''^ 


m ° 


t— 1 


1-5 ?i 





P4 




^gi 




(tn the 
, includir 
visible Se 
rse) Co 








P 


iJ ^ ^ ?> 




m 





§ 

o 
go 

l§ 

.-J Qi 



^ 2 



2s 

® ti_i 
too© 



OGQ 
O 

<5 



> tt 



^ bO 

<» o 
<;:) O 

-a 






P4 O 



a® 

o 
02 






o 
>» o 



O 
m 



o 
m 

O — 



_ o 



GQ 



So 



;. . M 



03 <j 



o 
o 



a! 



^ ^ O 



^ as . 

"I -Ss^ 



:^ 



'^ o g 
-OBu Vi 5 









<D fi S 

J- cS c8 
cS beg 

O 

P^ 






5>t 



EXPLANATION OF OUTLINE. 



In the preceding table or "Outline of the Sciences" we have 
advanced from the term of least comprehension and greatest ex- 
tension, namely, the term, Being. That which is represented by 
the term or concept Being supplies the subject-matter for On- 
tology, the Science of Being. 

We go on trying to increase the comprehension and diminish 
the extension by adding the terms, Finite and Infinite, to 
Being. The division is not one of genus into species, as we have 
seen when speaking of analogy (Nos. 28, 36), yet it serves us 
for this very broad outline. Infinite Being is the subject-mat- 
ter of the science called, in philosophy, Natural Theology. 

Continuing with Finite Being, increasing comprehension and 
diminishing extension, we have, in a perfect division, Substan- 
tial Finite Being and Accidental Finite Being. Ontology 
extends thus far, defining the notions of Infinite and Finite, 
and treating of Substance and of all that is not Substance, that 
is of Accident; quantity, quality, action, time, space, etc. It is 
general philosophy. 

Again dividing, and increasing comprehension, we have Ma- 
terial Substantial Finite Being and Spiritual Substantial 
Finite Being. We do not treat of bodiless spirit under the 
Finite, in philosophy. But taking the Material, in the wide 
sense of the term, we have the subject-matter of the science, 
Cosmology. 

Increasing the comprehension, again, by adding Animate and 
Inanimate, we get in the Animate Material, etc., the subject- 
matter of the science. Biology, as general science of life. If 
we take the other subdivision, Inanimate Material, etc. ,we find 
that range of sciences which treat of inanimate, inorganic mat- 
ter: Physics, etc. 

We leave the Inanimate; and we divide the Animate, by 
adding to the comprehension, into the Rational and the Irra- 
tional. The Irrational divided by adding to comprehension, 
gives us Sensitive and Non-Sensitive (the brute and the 
plant), with the sciences, Sensation, etc., Vegetation, etc. 

Returning to Rational Animate, etc., we find here the sci- 
ence of Man in general, or Anthropology. From this 
point forward we are engaged solely with Man. We can no 
longer divide into species. We use such divisions as will give 
us a complete and clear view of the subject, Man. 

By actual physical essential division (No. 146) we can divide 
Man into Soul and Animal Body. The Animal Body, for 

103 



104 LAWS OF THOUGHT 



general principles, we refer over to Sensation. Soul is the sub- 
ject-matter of the Science, Psychology. Psychology will treat 
of the Nature of the Soul and the Powers of the Soul. The 
Powers of the Soul, we group nder three headings : Power of 
actuating sense-perception, etc.; Intellect; Free-Will. 

Intellect, we consider in its Nature; its Method of Work; its 
Supply of Material. The Method of Work constitutes the ob- 
ject (or subject-matter) of the Science, Formal Logic. The 
Supply of Material for true thought gives us the object of the 
Science, Material Logic. 

Under the heading of Free Will we treat of the Existence 
and Nature of Free Will ; of the Norma or Rule of the Free 
Act; and of Practical Morality. The Existence and Nature of 
Free Will, we may readily refer to the treatise on the Powers 
of the Soul. In this way, accepting Free Will from Psychology, 
we have, left, the Norma of Free Act and Practical Morality. 
These last two. Norma and Practice, taken together, form the 
subject-matter of the Science, Ethics. 

This is one presentation of the philosophical and subsidiary 
sciences. In studying, we begin upon the lawest line with 
Formal Logic. Next, we take up Material Logic. Thus 
equipped, we go back to Ontology, and follow down through 
the Finite until we reach the border line of Ethics. Here, we 
turn back to take up the study of Natural Theology, which we 
had omitted and for which we are now prepared. At length, 
with what philosophy can teach us of God and man and of the 
wide universe about us, we study, in Ethics, the practical con- 
clusions to be drawn from the whole, to guide the actions of the 
free, intelligent being, Man. 

POINTS FOR PRACTICE. — The practical utility of 
Formal Logic, and the mental training to be derived from it, 
depend altogether upon the skill acquired in readily discerning 
the comprehension and extension of terms. The Laws of the 
Syllogism — Definition, Division, Synthesis, and Analysis — are 
all to be learned by the careful study of Extension and Com- 
prehension. Special attention should be given to these two 
correlated points. Original illustrations should be sought for as 
a proof that those in the book have been understood. 

(9) Name objects of the single apprehension or of the idea. 
(10) Give examples of judgments. (11) Upon what two prin- 
ciples does the mind work in reasoning? (13-15) What is a 
term, a proposition, a syllogism? (17-19) Give three classifica- 
tions of ideas. (19) Examples of singular, particular, collective, 
universal ideas. (20) How are universal ideas classified? What 
is meant by form, formality, or determination, in reference to 
idea? (21-27) Examples of species, genus, difference, property, 



POINTS FOR PRACTICE 105 

accident. (29) Name some forms that may be used both as 
generic and specific. (30) Give illustrations of highest genus, 
lowest species, subaltern genera. Tables of contents in scientific 
works will furnish examples. (32) Examples of real and logical 
terms. (33-35) Univocal and equivocal terms. (36) What is an 
analogous term? and why is the question of analogy introduced 
here? (37) Examples of the material, logical, real supposition 
of terms. (40) Examples of propositions, pointing out the sub- 
ject, copula, and predicate. (41) Examples showing the differ- 
ence between the logical and the grammatical predicate. (42) 
Examples of simple. (43) Compound. (45, 46) Categorical, 
conditional. (47, 48) Conjunctive and disjunctive propositions. 
Show how they are reducible to the conditional. (54, 55) Ex- 
amples of a priori and a posteriori judgments. Show why the 
a priori are called necessary, absolute, metaphysical, analytical; 
and the a posteriori, contingent, hypothetical, physical, synthet- 
ical. (59-61) What is meant by the extension and comprehension 
of terms or ideas? (62-63) What does the extension of a propo- 
sition depend upon? Examples of the four extensions of propo- 
sitions. (65-70) Explain the laws which declare the extension of 
the predicate in universal and particular propositions, both 
affirmative and negative. Name and illustrate the one exception 
for the universal affirmative. (73) State what is absolutely 
necessary that a proposition may have the force of a negation. 
(76) Examples of the conversion of propositions, retaining and 
changing quantity and quality. (7S) Of opposition in quantity 
and quality. (84) Explain the difference between consequent and 
consequence. (86) Give the analysis of an (original) argument. 
(88) Explain the true, primary meaning of Middle Term. (92) 
What is meant by the Moods of the Syllogism? (94-102) Nine 
Laws of the Syllogism. Compose faulty arguments or syllogisms, 
and show how each law may be violated. (104-107) Examples 
of syllogisms. Show how the conjunctive and disjunctive are 
reduced to the conditional. (108-113) Examples of enthymeme, 
sorites, polysyllogism, epichirem, dilemma. (114-122) Difference 
between formal and material logic; between direct and indirect 
demonstration; between simple and compound; between the a 
priori and the a posteriori. (124) Example of complete induc- 
tion. (125) What is required for the validity of the incomplete 
induction? (129-138) Examples of various fallacies. (139-160) 
Material for the practical study of Method will be found in 
ordinary reading. Are the definitions comprehensive? Are the 
divisions logical, complete? Where is there analysis, synthesis, 
induction, deduction? 



ALPHABETICAL INDEX 



Numbers refer to Paragraphs, 



Abstract idea, 17 

Accident, inseparable and sep- 
arable, 26, 27. 
fallacy of, 132. 
Accidental form, 27. 
Adequate idea, 18. 
A dicto simpliciter, fallacy, 133. 
Affirmative proposition, 72. 
Analogy, argument from, 127. 
Analogous terms, 2>2>^ 36. 
Analysis, 140. 

illustration of, 147. 
and the negative proposition, 
149. 
and discovery, 160. 
Antecedent in syllogism, 83. 
Apprehension, simple, 9. 
'as an act, 9. 
as representative, 9. 
A priori demonstration, 117, 
121. 
judgment, 55. 
A posteriori demonstration, 
117, 122. 
judgment, 56. 
Argument, 11, 15, 80. 
analysis of, 86. 
basis of, 11, 85. 
styles of, 81. 
Argumentation, 11. 
Axioms, for extension and 
comprehension of terms, 
58. 
for argument, 11, 85. 

Begging the question, 130. 

Being, predication of, 28, 36. 

science of, 166. 



107 



Cause, fallacy of the, 135. 
Caution, 103. 
Clear idea, 18. 
Collective idea, 19. 
Collective proposition, 63. 
Complete idea, 18. 
Compound demonstration, 120. 
Comprehension and extension 
of terms, axiom, regard- 
ing, 58. 

of idea and term, 60, 61. 

and metaphysical parts, 145. 

explanation^ of, 151. 

and definition, 153. 
Comprehensive idea, 18. 
Concept, 9. 
Conclusion, 11, 86. 

value of, 116. 
Concrete idea, 17. 
Consequence, 84. 
Consequent, fallacy of, 134. 

in syllogism, 83. 
Conversion of propositions, 76. 

Declaration, 10. 
Deduction, 11, 123. 
Definition, nominal, real, de- 
scriptive, genetic, essen- 
tial, 152. 
physical, metaphysical, 153. 
and comprehension, 153. 
some rules for, 154. 
Demonstration, 116. 
direct, 117, 118. 
indirect, 117, 119. 
simple and compound, 120. 
a priori and a posteriori, 117, 
121, 122. 



108 



LAWS OF THOUGHT 



Determination or form, 20. 
Diagram of figures in syl- 
logism, 89, 90, 91. 

of genus, species, etc., 30. 

of definition and division, 
150. 

of propositions, 79. 

of sciences, 161. 

of seventh law for syllogism, 
100. 
Difference, specific, 25. 
Differential idea, 25. 
Dilemma, 81, 113. 
Direct demonstration, 117, 118. 

universal idea, 21. 
Distinct idea, 18. 
Division, made into logical 
parts, 155. 

into genus and species, 155. 

simple rule, 156. 

Elenchi, ignorantia, 131. 
Enthymeme, 81, 109. 
Epichirem, 81, 112. 
Equipollence of propositions, 

Equivalence of propositions, 

n. 

Equivocal terms, 33, 35. 
Example, argument from, 126. 
Extension of terms and ideas, 
59, 61. 
axiom, 58. 
of predicate, 66, 71. 
and logical parts, 146. 
explanation of, 151. 
Extremes, extreme major term, 
extreme minor term, 87, 
88. 
Evading the question, 131. 

Fallacies, 130-138. 
Fallacy, 116, 129. 
Figures of syllogism, 88-91. 
Form (formality or determi- 
nation), 20. 

specific, 22. 

generic, 24. 



accidental, 27. 

when both generic and spe- 
cific, 29. 
Formal logic, 2, 114, 115. 

Genera, subaltern, 31. 
Generic, 24. 
idea, 24. 

and specific, the same form, 
29. 
Genus, 24. 

highest, 31. 
Grammatical predicate, logical 
and, 41. 

Herschel, Sir W., 122. 
Highest genus, 31. 

Idea, 9. 

characteristics of, 18. 

classifications of ideas, 17-19. 

comprehension of, 60, 61. 

differential, 25. 

extension of, 59, 61. 

generic, 24. 

object of universal reflex, 
23. 

specific, 22. 
Ignorantia elenchi, 131. 
Indirect demonstration, 117, 

119. 
Induction, 123. 

complete, 124. 

incomplete, 125. 
Inference, 11. 

Judgment, 10, Z^, 

as an act, 10. 

as representative, 10. 

immediate, 51. 

mediate, 52. 

a priori, necessary, absolute, 
metaphysical, analytical, 55. 

a posteriori, contingent, hy- 
pothetical, physical, syn- 
thetical, 56. 

synthetic a priori^ 57. 



ALPHABETICAL INDEX 



109 



Kant, 57. 

Knowledge, is representative, 

8. 
scientific knowledge, 139, 

157. 

Laws of extension of predi- 
cate, 71. 

of syllogism, 93-102. 
Leverrier, 122. 
Logic, artificial, 4. 

as an art, 6. 

as a science, 5. 

formal, 2, 114, 115. 

material, 2, 114, 115. 

natural, 3. 

the name, 1. 
Logical and grammatical pred- 
icate, 41. 

supposition of terms, 37. 
Lowest species, 31. 

Major extreme, 87, 88. 

premiss, 83, 88. 
Material logic, 2, 114, 115. 
Material supposition of terms, 

37. 
Method, scientific, 139. 

two processes, analysis and 
synthesis, 140. 
Mill, J. Stuart, 125. 
Mind, three acts of, 7. 
Minor extreme, %7, 88. 

premiss, SZ, 88. 
Moods of syllogism, 92. 

Negative particle, 72>. 

proposition, 72. 
Notion, 9. 

Object of a science, 158, 159. 

material, 159. 

formal, 159. 
Objections, fallacy of, 138. 
Objective, identity, 10. 
Ontology, 159. 



Opposition of propositions, 78. 
Oral expression of thought, 12. 

Paralogism, 116. 
Particular idea, 19. 

proposition, 63. 
Parts, real and logical, 141. 

accidental, integral, essen- 
tial, 142. 

physical, 143, 144. 

metaphysical, 143, 145. 

logical, 146. 

potential, 146. 

and comprehension, 145. 

and extension, 146. 

in scientific work, 146. 

and division, 155. 
Petitio principii, 130. 
Polysyllogism, 81, 111. 
Predicables, heads of, 28. 
Predicate of a proposition, 40, 
65. 

logical and grammatical, 41. 

laws of extension, 66-71. 
Premisses in syllogism, 83. 

major, S2», 88. 

minor, 83, 88. 
Principii petitio, 130. 
Property, 26. 
Proposition, 14, 39. 

simple, complex, 42; com- 
pound, 43. 

possible varieties of, 44. 

categorical, 45. 

conditional or hypothetical, 
46. 

conjunctive, 47. 

disjunctive, 48. 

extension of, singular, par- 
ticular, collective, univer- 
sal, 62, 63. 

use of name "particular," 64. 

extension of predicate in, 
66-71.^ 

affirmative, negative, 72. 

quality and quantity of, 74. 

relations of, conversion, 
equivalence or equipol- 
lence, opposition, 75-78. 



no 



LAWS OF THOUGHT 



Question, begging the, 130. 
fallacy of the, 136. 

Real supposition of terms, 

yi. 

Reasoning, 11, 80. 

as an act, as representative, 
two working principles, 11. 

process of, 53. 
Reference, fallacy of, 137. 
Reflex universal idea, 21. 

object of, 2Z, 

Science, 139, 157. 

object of a, 158. 

material and formal object, 
159. 

logical character of a, 160. 

analytic, synthetic, inductive, 
deductive, 160. 
Simple apprehension, 9. 

demonstration, 120. 
Singular idea, 19. 

proposition, 63. 
Sophism, 116. 
Sorites, 81, 110.- 
Species, 22, 23. 
Specific, 22. 

difference, 25. 

idea, 22. 

and generic, the same form, 
29. 
Subaltern genera, 31. 
Subject of a proposition, 40. 
Supposition of terms, real, ma- 
terial, logical, Zl . 
Syllogism, 15, 81, 82. 

antecedent, major and minor 
premiss, consequent in, 83. 

consequence in, 84. 

figures of, 88-91. 



moods of, 92. 

laws of, 93-102. 

simple, compound, condition- 
al, conjunctive, disjunctive, 
104-107. 
Synthesis, 140. 

illustration of, 148. 

and the negative proposition, 
149. 

and invention, 160. 
Synthetic a priori judgment, 
57. 

Table, analytic, 150. 

meaning of, 151. 
Terms, 13. 
classification and use, 32. 
univocal, equivocal, analo- 
gous, 33-36. 
comprehension and exten- 
sion, 59-61. 
extreme, extreme major, ex- 
treme minor, middle, 87. 
supposition of, real, materi- 
al, logical, 7)1, 
Thought, form of, 2. 
material of, 2. 
oral expression of, 12. 

Universal idea, 19. 

idea, direct, 21. 

idea, reflex, 21. 

idea, reflex, object of, 2Z. 

proposition, 63. 
Univocal terms, 33, 34. 

Whole, real, 141, 142. 
logical, 141, 146. 
physical, 143, 144. 
metaphysical, 143, 145. 



Deacidified using the Bookkeeper process. 
Neutralizing agent: Magnesium Oxide 
Treatment Date: Sept. 2004 

PreservationTechnologies 

A WORLD LEADER IN PAPER PRESERVATION 

1 1 1 Thomson Park Drive 
Cranberry Township. PA 16066 
(724)779-2111 



